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July 29, 2014

Search: Calculus - series

Number of results: 14,411

Calculus
By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B) 1-(2^2)/(2!)+(2^4)/(4!)-(2^6)/(6!)+...+((-1)^(k)2^(2k))/((2k)!) +...=
June 18, 2013 by Cole

Calculus
a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of convergence with x > 1; the power series ...
August 8, 2011 by laura

Calculus
Determine the following about the series. Indicate the test that was used and justify your answer. Sigma (lower index n = 1; upper index infinity) [sin((2n-1)pi/2)]/n A. The series diverges B. The series converges conditionally. C. The series converges absolutely. D. It cannot...
February 11, 2013 by Jenny

Calculus
Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...
April 21, 2010 by Megan

calculus
Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...
April 22, 2010 by Megan

calculus
Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...
April 22, 2010 by Megan

Calculus
How can I prove this series alternating series converges(this is the answer)? (-1)^2*(2/3)^n I tried it this way: an = (2/3)^n, then i just broke it down. 2^n/(3^n) and i took the ratio of it and got 2/3 which does not equal to one which would mean the series diverges.. but ...
July 26, 2013 by Isaac

College Calculus
Suppose the series An (from n=1 to INF) is known to be convergent. Prove that series 1/(An) (from n=1 to INF) is a divergent series. I have no idea what to do... please help!
March 24, 2008 by Mandy

College Calculus (Binomial Series)
Expand f(x) = (x+x^2)/((1-x)^3) as a power series and use it to find the sum of series (SUM from n=1 to infinity) (n^2)/(2^n) PLEASE HELP.
April 8, 2008 by Andrew

calculus
With power series, is an endpoint convergent if you plug it back into the original series, and get an alternating series that is conditionally convergent?
September 22, 2010 by Bob

Calculus
Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps? Also,do all power series start with a 1, as in (1+2x+4x^2+...)? Thanks in advance!
March 8, 2012 by W

Calculus
Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps? Also,do all power series start with a 1, as in (1+2x+4x^2+...)? Thanks in advance!
March 8, 2012 by W

calculus
Consider ∞ ∑ [(3k+5)/(kČ-2k)]ᵖ, for each p ∈ ℝ. k=3 Show this series { converges if p > 1 { diverges if p ≤ 1 Hint: Determine the known series whose terms past the second give an approximate match for the terms of this series. This series...
August 6, 2011 by Bernie

Calculus
Obtain the MacLaurin series for 1/(2-x) by making an appropriate substitution into the MacLaurin series for 1/(1-x). ------------ The MacLaurin series for 1/(1-x) = Σ x^k I substitue (x-1) in for x, because 1/(2-x) = 1/(1-(x-1)) Making the same substitution in the ...
June 25, 2009 by Sean

calculus
in the following series x is a real number. In each case use the ratio test to determine the radius of convergence of the series. Analyze the behavior of the series at the endpoints in order to determine the interval of convergence. A) (nx^n)/(n^2 + 2) B)((n^2)(x-2)^n)/2^n C...
April 12, 2014 by maggie

Calculus - Taylor #2
Find the Taylor series for f(x) centered at the given value of 'a'. (Assume that 'f' has a power series expansion. Do not show that Rn(x)-->0.) f(x) = x3, a = -1 and what i've done so far: f (x) = x^3 f ' (x) = 3x^2 f '' (x) = 6x^1 f ''' (x) = 6x f (-1) = -1 f ' (-1) = 3 f...
July 28, 2007 by COFFEE

CALCULUS-URGENT
find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)
March 4, 2008 by jane

CALCULUS
find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)
March 4, 2008 by jane

Calculus
does infinite power series -1/n diverge? (i think so, because it is just the negative of the harmonic series)...? thank you!
October 20, 2012 by Nikky

Calculus 2
Hello, I don't know what test to use for this series: Determine the sum of the following series: inf E n=1 (2^n + 9^n) / 12^n thank you!
March 22, 2013 by Tom

CALCULUS-URGENT- no one will respond!!!
find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)
March 5, 2008 by jane

Calculus, series
I cannot figure this out! What is the series (the Pattern) of this sequence? {1,5,1,5,1,5,1,5.......}
January 9, 2008 by Candace

calculus
how do you find the sum of a series? for example: the series from n=0 to infinity of (-1)^n/n!??? thanks
March 20, 2008 by sarah

calculus
Use division of power series to find the first three terms of the Maclaurin series for y = sec x.
August 1, 2011 by ami

calculus
I need help understanding how the series of e derives into the exponential series using the binomial theorem. Here is a link to a pic of a page in my book, regarding the exponential series: ht tp://i46.tiny pic(.)(com)/qz0oat . jpg (remove parentheses and spaces) A couple of ...
June 5, 2010 by Jimmy

calculus
state the power series of an appropriate familiar function and use it to calculate the power series of the given function. give answer in sigma notation. All power series have center at 0. f(x)=(e^(-x)^2) -1+(x^2) and g(x)=x cos (x/square root 3)
April 20, 2009 by pervaiz

Calculus
Show that the following series is absolutely convergent: Summation from 1 to infinity: [(-1)^n * (n+1) * 3^n]/ [2^(2n+1)] I've done the ratio test and replaced n in this series with n+1. I get 3/4 in the end, which is less than 1, which confirms that the series is abs. ...
March 24, 2012 by Anonymous

calculus
i have to determine whether the series is convergent, and if, find the sum the series is from k=1 to infinity of 2/((k+1)(k+3)) I got 5/6 as my answer and didn't know if it was right...
February 21, 2008 by sarah

calculus
what does this series, if it converges, converge to? the series from n=1 to infinity of (2^n + (-1)^n)/3^n
March 17, 2008 by sarah

calculus
Use multiplication of power series to find the first three non-zero terms of the Maclaurin series of e^x ln(1 − x).
August 1, 2011 by amber

Calculus
If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be? I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1
September 20, 2011 by Anonymous

Calculus - - Reiny
If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be? I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1
September 20, 2011 by Anonymous

calculus
test the series for convergence or divergence the series from n=0 to infinity of (x^2+1)/(x^3+1) I said that due to the limit comparison test this converges at 1
March 16, 2008 by lila

calculus
test the series for convergence or divergence the series from n=0 to infinity of sin (2^-x) I wasn't sure what test to use to see if this was or wasn't convergent
March 16, 2008 by lila

calculus
determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6
February 21, 2008 by sarah

calculus
test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?
February 27, 2008 by sarah

calculus
test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?
February 28, 2008 by laura

calculus
Show that the series(−1)^n−1(bn) where bn = 1/(n^1/2) if n is odd and bn = 1/2^n if n is even, diverges. Why does the alternating series test fail?
July 31, 2011 by amber

Calculus
If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY? Or should you do alternate series test also to say ...
March 4, 2007 by Jin

calculus
Another problem: determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6
February 21, 2008 by sarah

Pre-calculus
Which of the following series is divergent? a) 1+3(1/4)+9(1/4)^2+27(1/4)^3... b) 1+3(1/5)+9(1/5)^2+27(1/5)^3... c) 1+3(1/7)+9(1/7)^2+27(1/7)^3... d) 1+3(1/2)+9(1/2)^2+27(1/2)^3... How do you determine if a series in convergent or divergent??? The book that I have is about as ...
October 13, 2008 by Lucy

calculus
for each series determine if the series is absolutely convergent and convergent the sum from 0 to infinity of (-1)^n/(the square root of (n+1))
March 2, 2008 by sarah

calculus
test the series for convergence or divergence the series from n=1 to infinity of 1/(arctan(2n)) I again didn't know what test to use
March 16, 2008 by lila

calculus
does this series converge, and if so is it absolutely convergent? the series from n=1 to infinity of ((-1)^*n+1))/n^4 I found that by the ratio test it was inconclusive, so no abs. conv is this right? and how do i know if it is simply convergent?
March 17, 2008 by matt

calculus
does this series converge, and if so is it absolutely convergent? the series from n=1 to infinity of ((-1)^*n+1))/n^4 I found that by the ratio test it was inconclusive, so no abs. conv is this right? and how do i know if it is simply convergent?
March 17, 2008 by matt

Calculus 2
The following function has a series of the form the sum from n=0 to infinity of c(subn)x^n. Calculate the coefficients c(subn) and express the power series in summation notation. f(x)=(pi*x)/(pi*x+1) Thank you so much for your help!!!!
November 28, 2012 by Heather

Calculus
Consider an infinite series of the form (+-)3(+-)1(+-)1/3(+-)1/9(+-)1/27(+-)....(+-)1/3^n(+-)... The number 3,1, etc. are given but you will decide what the signs should be. a)Can you choose the signs to make the series diverge? B)Can you choose the signs to make the series ...
November 12, 2012 by oci

Calculus Derivative- Taylor Series?
let f(x)= x/x-1 find f'(x) f ''(x) and a formula for f ^ (n) * x. I found the first and second derivatives but do not know how to make a general equation for this. I have not learnt the Taylor or Maclaurin Series either. Thank you.
March 10, 2013 by Lisa

calculus
Where did the exponential series come from? 1 + x + x^2/2! + x^3/3!... Where did that number come from? and how is it used to get the trigonometric series?
May 31, 2010 by Miranda

calculus - power series ASAP please :)
using power series, integrate & evaluate to 4 dec. places integral from 0 to 1: sin x^2 dx i'm REALLY stuck on this. and i need help asap.. what is the inverse of "sin x^2" so that i could have it in a fraction that will fit the power series equation? and that is: (A)/(1-R) ...
July 31, 2007 by COFFEE

Excel Help
3) __________ are used to compare sets of data in one chart. Time series Multiple data series Relative series Comparison series Is multiple data series
July 12, 2009 by Bryan

calculus
use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... with a radius...
March 18, 2008 by meg

calculus
use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... with a radius...
March 19, 2008 by meg

calculus
How do you differentiate the maclaurin series for 1/(1-x) twice to find the maclaurin series of 1/(1-x)^3.
April 26, 2010 by Paul

Calculus
This is going to be pretty hard to show as text since it would be easier for me to post a picture of the question. The question has f(x) = x/4^2 - (2x^3)/4^4 + (3x^5)/4^6 + ... . I am trying to find out the value of f(2). There is a hint to differentiate the power series ...
October 4, 2010 by Douglas

calculus
determine whether the series converges of diverges the sum from k=2 to infinity of (the square root of (ln(k)))/k I said that because you can't integrate the series (goes to infinity) it diverges
February 26, 2008 by sarah

calculus
determine whether the series converges of diverges the sum from k=2 to infinity of (the square root of (ln(k)))/k I said that because you can't integrate the series (goes to infinity) it diverges is this true?
February 26, 2008 by sarah

calculus
determine if the series is absolutely convergent and convergent the sum from n=1 to infinity of sin(n^2)/n^2 what series test should I use and how? the ratio test?
March 2, 2008 by sarah

CALCULUS
find the radius and interval of convergence for the series the series from n=1 to infinity of ((-1)^(n+1)*x^n)/n! I did the ratio test so I had the Lim as n approaches infinity of -x/(n+1), but this is 0, giving no radius, so I think I did something wrong...
March 4, 2008 by jane

CALCULUS-URGENT
find the radius and interval of convergence for the series the series from n=1 to infinity of ((-1)^(n+1)*x^n)/n! I did the ratio test so I had the Lim as n approaches infinity of -x/(n+1), but this is 0, giving no radius, so I think I did something wrong...
March 4, 2008 by jane

Calculus 2
Find the radius of convergence and interval of convergence of the series. n=2 series to infinity (-1)^n * x^n+6/n+7 R= ? I= (or[ , ]or) How do i do this?? ( means convergent and [ means divergent.
November 5, 2012 by James

CALCULUS-URGENT- no one will respond!!!
find the radius and interval of convergence for the series the series from n=1 to infinity of ((-1)^(n+1)*x^n)/n! I did the ratio test so I had the Lim as n approaches infinity of -x/(n+1), but this is 0, giving no radius, so I think I did something wrong...
March 5, 2008 by laura

Calculus - series
I'm getting this answer wrong, can someone please help show me what i'm missing?? thank you :) Infinity of the summation n=0: [(-1)^n pi^(2n)] / [6^(2n) (2n)!] this is my work: [(-1^0) pi^(2*0)] / [6^(2*0) (2*0)!] + [(-1^1) pi^(2*1)] / [6^(2*1) (2*1)!] + [(-1^2) pi^(2*2)] / [6...
July 28, 2007 by COFFEE

Chemistry
Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (...
November 10, 2013 by Andy

math
for this infinite series (-1)^n/n^2 if i use alternating series test to show that sequence does of a^n does not go to 0, then does this mean that this series is diverging
July 27, 2010 by eng

Arithmetic Series - - Reiny
Consider the series defined by Sn = 3n-1 Find the first four terms of the series. How exactly do I do this?
September 12, 2011 by Anonymous

math
hi if i wanna find the Maclaurin series from another existing series by integrating that series , do i need to include the constant of integration ?? Thanks
May 16, 2010 by William

math
the last two tems in a geometric series are 1080 and 6480 and the sum ofthe series is 7775 what is the first term in the series
December 18, 2011 by Heather

calculus
determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges is this true?
February 26, 2008 by sarah

Calculus
Can someone prove (informally) the following theory: If there is a differentiable function, f, that is represented by a Taylor series, T, then the convergence interval for series T is identical to the convergence interval for the term-by-term derivative T'.
June 22, 2009 by Sean

calculus
determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges
February 26, 2008 by sarah

calculus
is this correct? use the integral test to determine if this series is convergent or divergent: the series from n=2 to infinity of 1/(n*square root of (ln(n))) I said it was divergent because the integral went to infinity
March 16, 2008 by john

chemistry
Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (nf...
November 10, 2013 by a.m

Calculus
In calculus, the sum of an infinite geometric series whose first term is 1/20 is given by the complex fraction 1/20 _____ 1-r where r is the common ratio between the terms. Simplify this expression.
March 15, 2010 by Anonymous

Chemistry
Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (...
November 10, 2013 by Andy

Calculus!!!
I need your help... I've posted this question a while ago but no one has answered it yet. Please please help me. Which of the following series can be used to compute ln(.8)? a) ln(x-1) expanded about x=0 b) lnx about x=0 c) ln x in powers of (x-1) d) ln(x-1) in powers of (x-1...
March 19, 2007 by Joan

Calculus III
Which of the following series are geometric series? Find the sum if they are 1. Infinity (Summation sign) n = 1 1/6n^2 2. Infinity (Summation sign) n = 1 (0.6)^n-1
December 10, 2007 by kile

calculus
for each series determine if the series is absolutely convergent and convergent the sum from 0 to infinity of (-1)^n/(the square root of (n+1)) I did the ratio test and got -1, which is less than 0 making it absolutely convergent, but do i need to take the absolute value of -...
March 2, 2008 by sarah

Calculus II
(a) Use differentiation to find power series representation for f(x)=1/(1+x)^2 What is the radius of convergence? (b) Use part (a) to find a power series for f(x)=1/(1+x)^3 (c) Use part (b) to find a power series for f(x)=x^2/(1+x)^3 I found part (a) which was Σ n=0 to &#...
November 16, 2010 by Anonymous

Math (College Level Mathematics)
Fourier sin series for f(x) = 1, 0 < x < Pie is given by 1 = 4/n E 1/ (2n-1) times sin (2n-1) x, (0 < x < n). Using this, find the Fourier sinc series for f(x)= 1, on 0 < x < c where c > 0. Then find the Fourier series for g(x), x > 0 where g(x) = 1, 0...
September 21, 2013 by Joy

calculus repost, please assist pleassssssse
Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=5-9((x-2)^2)-3((x-2)^3) to approximate the f(0) ???? I realize that Taylor series f(x)=f(a)+f'(a)(x-a)+f''(a)((x-a)^2)etc... but the above T(x) is centered at x=2, ...
March 15, 2011 by kiksy

Calculus 2
Calculate c(sub0), c(sub1), c(sub2), c(sub3), and c(sub4) for the power series the sum from n=0 to infinity of c(subn)x^n that represents f(x)=tanx. Use the first two nonzero terms of the series to approximate the tangent of 1/4 radian. Compare your approximation with the ...
November 28, 2012 by Heather

Calculus
how do I know if the series ln(n)/(2n) is DV or CV?
December 1, 2008 by Shaniquaa

Chemistry (Need) 7:00
What characterizes the electron configurations of transition metals such as silver and iron? Thanks Alot in Advance.. Fe is in the 3d transition series and Ag is in the 4d series. Thus, the distinguishing electron for the 3d series enters the 3d orbital while those for the 4d ...
November 12, 2006 by Lance

math
sorry for before it is my first time using this website and this is the real question in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62813. How many terms are in the series?
June 3, 2013 by Bob

Calc II
Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which converges, give an approximation of its sum, ...
November 7, 2012 by Lauren

Calculus II
Does anyone know of a very good website that can teach me to better understand the disk, washer, shell method to finding volume of irregular figures (solid of revolution)using of course, integration techniques (such as when to recognize integration with respect to y or X for ...
January 13, 2007 by EinstNewtLieb

calculus
for the series is absolutely convergent and convergent the series from 1 to infinity of (x^3)/(5^x) i did the ration test and get absolutely convergent and convergent is this correct?
March 2, 2008 by sarah

calculus
for the series is absolutely convergent and convergent the series from 1 to infinity of (x^3)/(5^x) i did the ration test and get absolutely convergent and convergent is this correct?
March 2, 2008 by sarah

Data managment math
5: In the best-of -five hockey series , the probability of winning the next game increases for each team by 0.1 if the previous game was won. If the teams ,the Ironmen and the Mustangs ,are in such a series and at the start of the series are evenly matched, what is the ...
January 28, 2008 by Samir

trig
for the geometric series shown, state whether the series in convergent. If the series is convergent, give the sum 9 +6.3 + 4.41
November 10, 2008 by jerson

Calculus
How do I prove that the series ln(n)/(3n) is divergent?
December 2, 2008 by Shaniquaa

Calculus
Is the series (8+1^n)/(1+2^n) divergent or convergent?
December 4, 2008 by Shaniquaa

calculus
Find the fourier series of F(x) = 1, -L<=x<0 = 0, 0<=<L f(x+2L) = f(x)
April 27, 2010 by ethan

calculus
find taylor series... a.f(x)=x^3-2x+4,a=2
November 7, 2010 by daan

Calculus
Represent f(x)= (e^x -1)/x as a power series.
December 3, 2010 by Linda

calculus
Find the sum of the series 2 + 9/2! + 27/3! + 81/4! . . .
August 8, 2011 by julia

calculus
find the taylor series f(x)1/2(e^x + e^-x) ;x=0
June 4, 2012 by soffy

Calculus II
Is the series 1/(n(n+1)) convergent? n=2 to n=infinity
March 25, 2013 by Sara

Calculus
Is the series 1/(n(n+1)) convergent? n=2 to n=infinity
March 25, 2013 by Liz

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