okay we started Flatland!! whohoo! today we took our first quiz, it was pretty easy. Flatland is about a 3d square in a 2d universe, these first few chapter talk about the nature of flatland and how everything looks like a flatline on a white piece of paper, it also says that depending on your shape shows what class in society your in. Moving up in society is not impossible, but it is very hard. also when males pass females they must always let them pass on the north side. it is also very hard for them to distinguish north south east and west, but the force ( kind of like gravity to us) is always a south ward pull, but it is harder for the inhabitants in temperate climates to figure it out. the inhabitants can go from triangles, hexagons, pentagons and so on.
okay... mrs. robinson hope everything goes well these next few weeks! can't wait to see pictures of your baby girl!
Friday, February 12, 2010
Reflection
Finally its mardi gras holidays! this week in adv math we took a chapter 13 test which was pretty simple because all it was sequences, and series, and sigma notation. I understood mostly the sum sequences for arithmetic and geometric stuff. Also, we started the book Flatland, kind of boring. But its about these squares and rectangles and triangles, and pentagons, and hexagons that all live in this little place called Flatland. There lifestyle is judged by the way they are shaped, like upper, lower, and middle classes. Also the women in the book flatland are treated unequally from the men. For example they have to enter through different doors than others. Well thats all i got out of Chapters 1-4, i guess we got read more when we get back from the holidays.
Tuesday, February 9, 2010
Reflection 25
Okay, so I know I'm doing this late, but I'm just getting over the hype from the Super Bowl, and may I say WHO DAT?!?! Gotta love the Saints. Last week we learned a lot in math about sequences and series. We learned about limits.
Limits are denoted as lim with and n (arrow) infinity underneath it.
Here are the rules:
1. lim(n infinity) - if the degree of the top = the degree of the bottom then the answer is the coefficients
2. If the degree of the top is greater than the degree of the bottom, then it is infinity
3. If the degree of the top is smaller than the degree of the bottom, then it is 0.
IF the rules don't apply, you will have to use your calculator to find what the sequence is approaching.
For a geometric sequence if the absolute value of r is less than 1, then it goes to 0.
Examples:
lim (n infinity) sin (1/n)
sin(1/100) = .010
sin(1/1000) = .0010
sin(1/10000) = .00010
lim (n infinity) n+5/n = 1, because the degree is the same, so the coefficients equal 1
The only thing I really still don't get are the sigma notation, where you have to express the series in sigma notation. Example problems please?
Limits are denoted as lim with and n (arrow) infinity underneath it.
Here are the rules:
1. lim(n infinity) - if the degree of the top = the degree of the bottom then the answer is the coefficients
2. If the degree of the top is greater than the degree of the bottom, then it is infinity
3. If the degree of the top is smaller than the degree of the bottom, then it is 0.
IF the rules don't apply, you will have to use your calculator to find what the sequence is approaching.
For a geometric sequence if the absolute value of r is less than 1, then it goes to 0.
Examples:
lim (n infinity) sin (1/n)
sin(1/100) = .010
sin(1/1000) = .0010
sin(1/10000) = .00010
lim (n infinity) n+5/n = 1, because the degree is the same, so the coefficients equal 1
The only thing I really still don't get are the sigma notation, where you have to express the series in sigma notation. Example problems please?
reflection for 2/7
so ya, the saints won the superbowl!
WHO DAT!
and peyton didnt shake hands with the players!
what a n00b!
haha
k, now its math time
ok, so the basics for infinite series are pretty easy
sum of the infinite series
9-6+4=
r=-6/9 - -2/3 r= 4/-6 = -2/3
-2/3<1
s=9/(1-(-2/3)) = 27/5
where the values of x converge
1+(x-2)+(x-2)^2+(x-2)^3+
r=x-2
x-2<1
-1<1
1<3
.4545454545 as a fraction
45/100-1
= 45/99
= 5/11
ya, pretty basic and easy right?
WRONG!
it took me a while to figure this stuff out!
ARGH! DEFF HATE THIS CHAPTER!
anyways, what i rly didnt understand too much was the ∑ notation stuff,
the only thing that's good that contains ∑ in it is Ninja Gaiden ∑ II
thats it!
i rly need help with this one!
WHO DAT!
and peyton didnt shake hands with the players!
what a n00b!
haha
k, now its math time
ok, so the basics for infinite series are pretty easy
sum of the infinite series
9-6+4=
r=-6/9 - -2/3 r= 4/-6 = -2/3
-2/3<1
s=9/(1-(-2/3)) = 27/5
where the values of x converge
1+(x-2)+(x-2)^2+(x-2)^3+
r=x-2
x-2<1
-1<1
1<3
.4545454545 as a fraction
45/100-1
= 45/99
= 5/11
ya, pretty basic and easy right?
WRONG!
it took me a while to figure this stuff out!
ARGH! DEFF HATE THIS CHAPTER!
anyways, what i rly didnt understand too much was the ∑ notation stuff,
the only thing that's good that contains ∑ in it is Ninja Gaiden ∑ II
thats it!
i rly need help with this one!
reflection for 2/1 or w/e that one was
aaaaaaahhhhhhhhhhhh
i hate bein sick! lol
anyways.....
we started on series......fun *sarcasm*.......but it wasnt all that bad......for the first day or so
let's start with formula review:
arithmetic sequence:
tn=t1+(n-1)d
*d being your ratio, or number that's added or subtracted.
*t1 being your first term
*n being the term in the sequence we're trying to find
ex:
In the arithmetic sequence:3,5,7,9-- find the 28th term.
t28=3+(27)(2)
t28=3+54
t28=57
geometric sequence, or a sequence with multiplication and division:
tn=t1*r^(n-1)
*t1 is first term.
*r is your ratio, multiplied or divided by.
*missing term.
ex:
In the geometric sequence: 2,4,8,16-- find the 10th term
t10= 2*2^9
t10= 2*512
t10= 1024
i mean, all this is pretty simple and easy, its just the bits and pieces of finding how certain numbers make a series!
u kno, somethin like 1-1/2+1/4-1/8…
u kno, complicated ones like that,
just need a little help with those kinds of series
i hate bein sick! lol
anyways.....
we started on series......fun *sarcasm*.......but it wasnt all that bad......for the first day or so
let's start with formula review:
arithmetic sequence:
tn=t1+(n-1)d
*d being your ratio, or number that's added or subtracted.
*t1 being your first term
*n being the term in the sequence we're trying to find
ex:
In the arithmetic sequence:3,5,7,9-- find the 28th term.
t28=3+(27)(2)
t28=3+54
t28=57
geometric sequence, or a sequence with multiplication and division:
tn=t1*r^(n-1)
*t1 is first term.
*r is your ratio, multiplied or divided by.
*missing term.
ex:
In the geometric sequence: 2,4,8,16-- find the 10th term
t10= 2*2^9
t10= 2*512
t10= 1024
i mean, all this is pretty simple and easy, its just the bits and pieces of finding how certain numbers make a series!
u kno, somethin like 1-1/2+1/4-1/8…
u kno, complicated ones like that,
just need a little help with those kinds of series
reflecttion... 2/7
umm, how bout that super bowl?!!
double and half angle formulas's
sin2(alpha)=2sin(alpha) cos(alpha)
cos2(alpha)=cos^2(alpha)-sin^2(alpha)=1-2sin^2(alpha)=2cos^2(alpha)-1
tan2(alpha)=2tan(alpha)/1-tan^2(alpha)
sin(alpha)/2= +or- sqrt of (1-cos(alpha)/2)
cos(alpha)/2=+or- sqrt of (1+cos(alpha)/2)
tan(alpha)/2=+or- sqrt of (1-cos(alpha)/1+cos(alpha)=sin(alpha)/1+cos(alpha)=1-cos(alpha)/sin(alpha)
Sum Formula for Tangent:
tan(alpha+beta)=tan(alpha)+tan(beta)/1-tan(alpha) tan(beta)
Sum and Difference Formulas for Cosine and Sine:
cos(alpha+or-beta)=cos(alpha) cos(beta)-or+sin(alpha) sin(beta)
sin(alpha+or-beta)=sin(alpha) cos(beta)+or-cos(alpha) sin(beta)
just remember for these formulas that some of the signs are not the same throughout the entire formula, thats why it is important to memorize these formulas.. that and on the tests you are supposed to write every formula you use by the problem ;)
double and half angle formulas's
sin2(alpha)=2sin(alpha) cos(alpha)
cos2(alpha)=cos^2(alpha)-sin^2(alpha)=1-2sin^2(alpha)=2cos^2(alpha)-1
tan2(alpha)=2tan(alpha)/1-tan^2(alpha)
sin(alpha)/2= +or- sqrt of (1-cos(alpha)/2)
cos(alpha)/2=+or- sqrt of (1+cos(alpha)/2)
tan(alpha)/2=+or- sqrt of (1-cos(alpha)/1+cos(alpha)=sin(alpha)/1+cos(alpha)=1-cos(alpha)/sin(alpha)
Sum Formula for Tangent:
tan(alpha+beta)=tan(alpha)+tan(beta)/1-tan(alpha) tan(beta)
Sum and Difference Formulas for Cosine and Sine:
cos(alpha+or-beta)=cos(alpha) cos(beta)-or+sin(alpha) sin(beta)
sin(alpha+or-beta)=sin(alpha) cos(beta)+or-cos(alpha) sin(beta)
just remember for these formulas that some of the signs are not the same throughout the entire formula, thats why it is important to memorize these formulas.. that and on the tests you are supposed to write every formula you use by the problem ;)
2/7
We learned about arithmetic and geometric formula this week in chapter 13, this is to find a certain number in a sequence of numbers.
Arithmetic formula:
a.n = a.1 + (n-1)d
Geometric formula:
a.n = a.1 x r^(n-1)
r = what you multiply by
An example of an arithmetic sequence is:
1,3,5,7....
An example of a geometric sequence is:
3.25, 5.5, 7.75, ...
To find these a certain number in these sequences you just use the formulas and plug in.
Arithmetic formula:
a.n = a.1 + (n-1)d
Geometric formula:
a.n = a.1 x r^(n-1)
r = what you multiply by
An example of an arithmetic sequence is:
1,3,5,7....
An example of a geometric sequence is:
3.25, 5.5, 7.75, ...
To find these a certain number in these sequences you just use the formulas and plug in.
Monday, February 8, 2010
Reflection
Saints won the superbowl
who dat!!!!!!!!!!! now on to my blog
Five Rules for Sequences and Series
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
In chapter 13 we learned about sequences, many formulas, sigma notation, etc.
Sigma Notation
100 - 1 & 100 are called the limits of summation.
sigma n^2 - n^2 is the summand
n=1 - the bottom variable is called the index, which is K.
- To evaluate-plug in the numbers between your limits of summation into the summand.
Adding each term to form a series.
- Examples:
Give each series in expanded form
Arithmetic formula:
tn = t1 + (n-1)d
n = term #
t1 = first term
d = what you add
Geometric to find a term
tn = t1 x r^(n-1)
r = what you multiply by
who dat!!!!!!!!!!! now on to my blog
Five Rules for Sequences and Series
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
In chapter 13 we learned about sequences, many formulas, sigma notation, etc.
Sigma Notation
100 - 1 & 100 are called the limits of summation.
sigma n^2 - n^2 is the summand
n=1 - the bottom variable is called the index, which is K.
- To evaluate-plug in the numbers between your limits of summation into the summand.
Adding each term to form a series.
- Examples:
Give each series in expanded form
Arithmetic formula:
tn = t1 + (n-1)d
n = term #
t1 = first term
d = what you add
Geometric to find a term
tn = t1 x r^(n-1)
r = what you multiply by
Relfection 25?
This week went by fast which was good :) & Saints won the superbowl..woooooohooo! ha.
I'm just explaining some of the stuff we learned in chapter 13 that I actually get.
* to find a term
arithmetic- tn = t1 + (n-1)d
where n=term #, t1=first term, d=what you add, tn=term you're looking for
geometric- tn = t1 x r^(n-1)
where r=what you multiply by
* to find the sum
arithmetic- sn = n(t1 + tn) / 2
geometric- sn = t1(1 - r^n) / 1-r
tn-1 = previous term
tn-2 = previous to the previous term
**Arithmetic sequences are when you have to add or subtract to get the next term. Geometric sequences are when you have to multiply to get the next term.
Examples:Find the formula for this arithmetic sequence:
3, 5, 7,...
tn = 3 + (n-1)2
tn = 3 + 2n - 2
tn = 1 + 2n
*These are easy you just plug in the previous term to get your answer.
You add 2 to each number to get the next number so plug 2 in for (n-1)
Solve, then you'll get the answer.
Find the next four numbers in the sequence:
t1 = 1 & tn = 3(tn-1) - 11, 2, 5, 14, 41,...
*For these you just keep plugging in the previous term. Start with t1 then go to
t4 plugging in the previous term for (tn-1)
Find the sum of the first ten terms of the series:
2 - 6 + 18 - 54 +...
s10 = 2(1 - (-3)^10) / 1 - (-3)
s10 = -29, 524
*(2 being the first number in the problem, -3 being what you multiply each number by
to get the next term)
Find the sum of the first 25 terms of the arithmetic series:
11 + 14 + 17 + 20 +...
tn = 11 +(25 - 1)3
tn = 83
s25 = 25(11 +83) / 2
s25 = 1175
*(11 being the first number in the sequence, 3 being the number you add, Plug 25 into the
n-1 formula because your looking for the 25th term)
I'm just explaining some of the stuff we learned in chapter 13 that I actually get.
* to find a term
arithmetic- tn = t1 + (n-1)d
where n=term #, t1=first term, d=what you add, tn=term you're looking for
geometric- tn = t1 x r^(n-1)
where r=what you multiply by
* to find the sum
arithmetic- sn = n(t1 + tn) / 2
geometric- sn = t1(1 - r^n) / 1-r
tn-1 = previous term
tn-2 = previous to the previous term
**Arithmetic sequences are when you have to add or subtract to get the next term. Geometric sequences are when you have to multiply to get the next term.
Examples:Find the formula for this arithmetic sequence:
3, 5, 7,...
tn = 3 + (n-1)2
tn = 3 + 2n - 2
tn = 1 + 2n
*These are easy you just plug in the previous term to get your answer.
You add 2 to each number to get the next number so plug 2 in for (n-1)
Solve, then you'll get the answer.
Find the next four numbers in the sequence:
t1 = 1 & tn = 3(tn-1) - 11, 2, 5, 14, 41,...
*For these you just keep plugging in the previous term. Start with t1 then go to
t4 plugging in the previous term for (tn-1)
Find the sum of the first ten terms of the series:
2 - 6 + 18 - 54 +...
s10 = 2(1 - (-3)^10) / 1 - (-3)
s10 = -29, 524
*(2 being the first number in the problem, -3 being what you multiply each number by
to get the next term)
Find the sum of the first 25 terms of the arithmetic series:
11 + 14 + 17 + 20 +...
tn = 11 +(25 - 1)3
tn = 83
s25 = 25(11 +83) / 2
s25 = 1175
*(11 being the first number in the sequence, 3 being the number you add, Plug 25 into the
n-1 formula because your looking for the 25th term)
Sunday, February 7, 2010
Super Booooooowl Reflection
Let's go back over some ole stuff: Inequalities!
3x-1>2
You just add one to both sides...
3x>3...
and then you divide by three on both sides...
x>1...
and that is your answer. But you have to remeber if you multiply or divide by a negative number, then you have to switch the signs.
For example,-2x+1>3
You would subtract one from both sides...
-2x>2
and then you would divide by negative two...
x<1...>
The absolute zero ones were easy too. If you have on greater than or less than, it is an OR, but if you have one that is greater than or equal to or less than or equal to, it is an AND. For example.(/) will be the absolute value sign/x-4/ <5
So you make two problems:x-4<5>-5 x<9>-1
Example of the AND problem:
/x-9/>or equal to 2
Instead of making two problems, you just add it to the front of the original problem:
-2>or=to x-9 >or=to 2
Then you add nine to all sides...
7>or=to x >or=to 11
So your final answer would be xor=to 11
And are we takin the chapter test tuesday?
3x-1>2
You just add one to both sides...
3x>3...
and then you divide by three on both sides...
x>1...
and that is your answer. But you have to remeber if you multiply or divide by a negative number, then you have to switch the signs.
For example,-2x+1>3
You would subtract one from both sides...
-2x>2
and then you would divide by negative two...
x<1...>
The absolute zero ones were easy too. If you have on greater than or less than, it is an OR, but if you have one that is greater than or equal to or less than or equal to, it is an AND. For example.(/) will be the absolute value sign/x-4/ <5
So you make two problems:x-4<5>-5 x<9>-1
Example of the AND problem:
/x-9/>or equal to 2
Instead of making two problems, you just add it to the front of the original problem:
-2>or=to x-9 >or=to 2
Then you add nine to all sides...
7>or=to x >or=to 11
So your final answer would be xor=to 11
And are we takin the chapter test tuesday?
reflection
The saints just won the super bowl:)))
mwahahahahhahahahaha!!
Infinite Sequences and Series...
Five Rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
3) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
Check it:
lim n -> infinity -10^n
RULE 4
-10^100 = 1.0 x 10^100 (aka very big number)
-10^1000 = 1.0 x 10^1000 (aka even bigger number)
-10^10000 = 1.0 x 10^10000 (aka very very big number)
The numbers are getting bigger and getting closer to infinity, so the answer is
-10^n = infinity
What i dont really know how to do is some of the more difficult versions of the question above but thats about it 0-o
Infinite Sequences and Series...
Five Rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
3) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
Check it:
lim n -> infinity -10^n
RULE 4
-10^100 = 1.0 x 10^100 (aka very big number)
-10^1000 = 1.0 x 10^1000 (aka even bigger number)
-10^10000 = 1.0 x 10^10000 (aka very very big number)
The numbers are getting bigger and getting closer to infinity, so the answer is
-10^n = infinity
What i dont really know how to do is some of the more difficult versions of the question above but thats about it 0-o
Reflection 25
SAINTS WON THE SUPERBOWL, KRUNK SUCKKK ITTTTTTT.
:)
for math,
sequences and series...
I don't know much, so ima say all i know.
formulas:
arithmetic formula:
an=a1+(n-1)(d)
geometric formula:
an=a1*r^n-1
EXAMPLES:
in an arithmetic sequence- 3,5,7 find the 12th term.
t12=3+*(11)(2)
t12=25
in a geometric sequence- 2,4,8 find the 10th term.
t10=2*2^9
t10=2048
and for what i don't know,
everything else!
:)
for math,
sequences and series...
I don't know much, so ima say all i know.
formulas:
arithmetic formula:
an=a1+(n-1)(d)
geometric formula:
an=a1*r^n-1
EXAMPLES:
in an arithmetic sequence- 3,5,7 find the 12th term.
t12=3+*(11)(2)
t12=25
in a geometric sequence- 2,4,8 find the 10th term.
t10=2*2^9
t10=2048
and for what i don't know,
everything else!
Reflection 25!
Mkayyyyy, so the SAINTS just won the SUPERBOWLLLLLLLL!
Stoked, or no?
And why do we still have blogs? NO SCHOOL TOMORROWWWWW!
Hmmm, for the math?
this week we learned all about Sequences and Series:
There are five rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer=the coefficients.
2) if the degree of the top is greater than the degree of the bottom, then the answer=infinity.
3) if the degree of the top is less than the degree of the bottom, then the answer=0.
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0.
Examples:
lim n -> infinity sin (1/n)
sin (1/100) = .01
sin (1/1000) = .001
sin (1/10000) = .0001
It is getting closer to 0, so the answer is:
sin (1/n) = 0
lim n -> infinity n^2 + 1/ 2n^2 - 3n
= 1/2
lim n -> infinity 5n^2 + n^1/2 / 3n^3 + 7
= 0
lim n -> infinity 7n^3 / 4n^2 - 5
= infinity
As for what i don't understand,
the chapter test number 6,7, & 11.
HELPPPPP?!
Stoked, or no?
And why do we still have blogs? NO SCHOOL TOMORROWWWWW!
Hmmm, for the math?
this week we learned all about Sequences and Series:
There are five rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer=the coefficients.
2) if the degree of the top is greater than the degree of the bottom, then the answer=infinity.
3) if the degree of the top is less than the degree of the bottom, then the answer=0.
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0.
Examples:
lim n -> infinity sin (1/n)
sin (1/100) = .01
sin (1/1000) = .001
sin (1/10000) = .0001
It is getting closer to 0, so the answer is:
sin (1/n) = 0
lim n -> infinity n^2 + 1/ 2n^2 - 3n
= 1/2
lim n -> infinity 5n^2 + n^1/2 / 3n^3 + 7
= 0
lim n -> infinity 7n^3 / 4n^2 - 5
= infinity
As for what i don't understand,
the chapter test number 6,7, & 11.
HELPPPPP?!
Reflection #25
Okay, to begin...everyone, watch out. I believe we have just seen a sure sign of the apocalypse...the Saints have won the superbowl!
Anyway, on to math:
Infinite Sequences and Series...
Five Rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
3) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
Examples:
lim n -> infinity sin (1/n)
RULE 4
sin (1/100) = .01
sin (1/1000) = .001
sin (1/10000) = .0001
It is getting closer to 0, so the answer is:
sin (1/n) = 0
lim n -> infinity n^2 + 1/ 2n^2 - 3n
RULE 1
= 1/2
lim n -> infinity 5n^2 + n^1/2 / 3n^3 + 7
RULE 3
= 0
lim n -> infinity 7n^3 / 4n^2 - 5
RULE 2
= infinity
lim n -> infinity -10^n
RULE 4
-10^100 = 1.0 x 10^100 (aka very big number)
-10^1000 = 1.0 x 10^1000 (aka even bigger number)
-10^10000 = 1.0 x 10^10000 (aka very very big number)
The numbers are getting bigger and getting closer to infinity, so the answer is
-10^n = infinity
** in the calculator, it may show up as overflow error, which means to number is too big to express
Now, what I don't know how to do...#6 on the ch. 13 test review in the book. Any help? I don't even know where to begin. If someone could work it for me, or show me a similar problem, that'd be a big help! ^^ GO SAINTS!
Anyway, on to math:
Infinite Sequences and Series...
Five Rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
3) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
Examples:
lim n -> infinity sin (1/n)
RULE 4
sin (1/100) = .01
sin (1/1000) = .001
sin (1/10000) = .0001
It is getting closer to 0, so the answer is:
sin (1/n) = 0
lim n -> infinity n^2 + 1/ 2n^2 - 3n
RULE 1
= 1/2
lim n -> infinity 5n^2 + n^1/2 / 3n^3 + 7
RULE 3
= 0
lim n -> infinity 7n^3 / 4n^2 - 5
RULE 2
= infinity
lim n -> infinity -10^n
RULE 4
-10^100 = 1.0 x 10^100 (aka very big number)
-10^1000 = 1.0 x 10^1000 (aka even bigger number)
-10^10000 = 1.0 x 10^10000 (aka very very big number)
The numbers are getting bigger and getting closer to infinity, so the answer is
-10^n = infinity
** in the calculator, it may show up as overflow error, which means to number is too big to express
Now, what I don't know how to do...#6 on the ch. 13 test review in the book. Any help? I don't even know where to begin. If someone could work it for me, or show me a similar problem, that'd be a big help! ^^ GO SAINTS!
Reflection
Infinite Sequences and Series...
Five Rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
3) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
Check it:
lim n -> infinity -10^n
RULE 4-10^100 = 1.0 x 10^100 (aka very big number)
-10^1000 = 1.0 x 10^1000 (aka even bigger number)
-10^10000 = 1.0 x 10^10000 (aka very very big number)
The numbers are getting bigger and getting closer to infinity, so the answer is
-10^n = infinity
im still confused on when she asks to find the number of multiples between two numbers...
Five Rules:
1) if the degree of the top is equal to the degree of the bottom, then the answer is the coefficients
2) if the degree of the top is greater than the degree of the bottom, then the answer is infinity
3) if the degree of the top is less than the degree of the bottom, then the answer is 0
4) If the previous rules don't apply, you will havve to use your calculator to find what the sequence is approaching (replacing 100, 1000, and 10000 for n)
5) for a geometric sequence, if the absolute value of r is less than 1, then it goes to 0
Check it:
lim n -> infinity -10^n
RULE 4-10^100 = 1.0 x 10^100 (aka very big number)
-10^1000 = 1.0 x 10^1000 (aka even bigger number)
-10^10000 = 1.0 x 10^10000 (aka very very big number)
The numbers are getting bigger and getting closer to infinity, so the answer is
-10^n = infinity
im still confused on when she asks to find the number of multiples between two numbers...
reflection 25?
So this week went by pretty fast. Chapter 13 is kind of easy, just some things are confusing to me. I thought Sums of Infinite Series was pretty easy. You only have one formula: s=t1/1-r.
Heres some examples on the sums of infinite series:
1) Find the sum of the infinite series
9-6+4=
r=-6/9 - -2/3 r= 4/-6 = -2/3
-2/3<1
s=9/(1-(-2/3)) = 27/5
2) For what values of x does the series converge?
1+(x-2)+(x-2)^2+(x-2)^3+
r=x-2
x-2<1
-1
3) Write .4545454545 as a fraction.
45/100-1
= 45/99
= 5/11
Those are very easy, all you have to do is put the numbers that repeat over whatever place they are in, like 10th, 100th, 1000th, etc. And then you just reduce them until you can't anymore and thats your answer.
Heres some examples on the sums of infinite series:
1) Find the sum of the infinite series
9-6+4=
r=-6/9 - -2/3 r= 4/-6 = -2/3
-2/3<1
s=9/(1-(-2/3)) = 27/5
2) For what values of x does the series converge?
1+(x-2)+(x-2)^2+(x-2)^3+
r=x-2
x-2<1
-1
3) Write .4545454545 as a fraction.
45/100-1
= 45/99
= 5/11
Those are very easy, all you have to do is put the numbers that repeat over whatever place they are in, like 10th, 100th, 1000th, etc. And then you just reduce them until you can't anymore and thats your answer.
Reflection #25
Okayyy, this is superbowl sundayyy! I really don't feel like doing a reflectionn. I want to watch the game, but i'm bored anyway. THe saints are going to win anyway, duhh. So i'm just going to review some of the arithmetic and geometric functions.
__________________________________________________________________
Find if arithmetic or geometric:
2,4,6,8,..
Arithmetic because you add two to the previous term to get the next term
1,2,6,3,...
Neither because 2+1 does not equal 6 and neither does 2*2
2,4,6,10...
Neither because 6+2 does not equal ten
1,3,9,27...
Geometric because you multiply the previous term by three to get the next term
2,-6,18,-54...
Geometric because you multiply the previous term by negative three to get the next term
________________________________________________________________
So, this is reeallyy reallyy easyyy. I actually do not need any help on this and hopefully i do great on the testtt! whoop whoop, but if anyone wants to give examplesss, GO FOR IT! WHO DAT?!
__________________________________________________________________
Find if arithmetic or geometric:
2,4,6,8,..
Arithmetic because you add two to the previous term to get the next term
1,2,6,3,...
Neither because 2+1 does not equal 6 and neither does 2*2
2,4,6,10...
Neither because 6+2 does not equal ten
1,3,9,27...
Geometric because you multiply the previous term by three to get the next term
2,-6,18,-54...
Geometric because you multiply the previous term by negative three to get the next term
________________________________________________________________
So, this is reeallyy reallyy easyyy. I actually do not need any help on this and hopefully i do great on the testtt! whoop whoop, but if anyone wants to give examplesss, GO FOR IT! WHO DAT?!
Reflection
I'm actually starting to get this stuff. yayyyyyyyyy. haha
here are the formulas followed by examples:
Arithmetic formula:
tn = t1 + (n-1)d
t2=4 d=1 find the 30th term. Well first you have to find t1 which will be t2-d so t1=3 now plug it into the formula 3+ 29*1 which = 32
Geometric to find a term
tn = t1 x r^(n-1)
Now if you were given t1=3 r=2 find the 8th term. All you do is plug it in your formula. and it will look like this 3*2^7 which will give you 768
Now this is something that shows up on every quiz we have and will be on the test.
State whether the following are Arithmetic, Geometric, or Neither.
2,4,6,8,...
Arithmetic because you add two to the previous term to get the next term
1,2,6,3,...
Neither because 2+1 does not equal 6 and neither does 2*2
2,4,6,10...
Neither because 6+2 does not equal ten
1,3,9,27...
Geometric because you multiply the previous term by three to get the next term
2,-6,18,-54...
Geometric because you multiply the previous term by negatvie three to get the next term
here are the formulas followed by examples:
Arithmetic formula:
tn = t1 + (n-1)d
t2=4 d=1 find the 30th term. Well first you have to find t1 which will be t2-d so t1=3 now plug it into the formula 3+ 29*1 which = 32
Geometric to find a term
tn = t1 x r^(n-1)
Now if you were given t1=3 r=2 find the 8th term. All you do is plug it in your formula. and it will look like this 3*2^7 which will give you 768
Now this is something that shows up on every quiz we have and will be on the test.
State whether the following are Arithmetic, Geometric, or Neither.
2,4,6,8,...
Arithmetic because you add two to the previous term to get the next term
1,2,6,3,...
Neither because 2+1 does not equal 6 and neither does 2*2
2,4,6,10...
Neither because 6+2 does not equal ten
1,3,9,27...
Geometric because you multiply the previous term by three to get the next term
2,-6,18,-54...
Geometric because you multiply the previous term by negatvie three to get the next term
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