Register to reply

Fouiers series Calculate sum

Share this thread:
Nov3-11, 09:24 AM
P: 169
1. The problem statement, all variables and given/known data
Consider the 2[itex]\pi[/itex]-periodic function f(t) = t t in [-Pi;Pi]
a) show that the real fouier series for f(t) is:
[itex]f(t) ~ \sum\limits_{n=1}^{\infty}\frac{2}{n}(-1)^{n+1}\sin nt[/itex]
Use the answer to evaluate the following : [itex]\sum\limits_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{2n-1}[/itex]
Hint: Use Fouier's law with t = [itex]\pi[/itex]/2

2. Relevant equations
Fouiers Law? I'm danish, and therefore i'm not really sure what it's called.

3. The attempt at a solution
Part a i have done by finding the coefficients.
Part b) I can't see where the problem in part b and the answer to a relates. I've tried with Maple 15 to calculate the value and i'm getting Pi/4, but i keep getting something different for the series from a)
Please Help me, i would really like to understand this as i'm studying physics.
Phys.Org News Partner Science news on
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Nov3-11, 10:57 AM
P: 6
The answer should be pi/4 ...

from fourier series we got ...

t = [itex]\sum\frac{2}{n}(-1)n+1sinnt[/itex]

for t = [itex]\frac{\pi}{2}[/itex] ,

[itex]\frac{\pi}{2}[/itex] = 2 - 2/3 + 2/5 - 2/9 + ......

which followed ,

[itex]\frac{\pi}{2}[/itex] = 2 * [itex]\sum\frac{(-1)n+1}{2n - 1}[/itex]

hence, [itex]\sum\frac{(-1)n+1}{2n - 1}[/itex] = [itex]\frac{\pi}{4}[/itex]
Nov3-11, 11:41 AM
P: 169
Hmm, isn't that a backwards proof? Can't i use something like the even terms of sin(n*Pi/2) = 0 and the odd ones alternates between -1 and 1

And how is t = ... isn't it f(t)?

Register to reply

Related Discussions
Calculate the sum of the series Calculus & Beyond Homework 3
Program which calculate a sum of series [C++] Engineering, Comp Sci, & Technology Homework 1
Fourier series and calculate integral Calculus & Beyond Homework 2
Complex power series to calculate Fourier series Calculus & Beyond Homework 1
How to calculate this series Calculus 5