(adsbygoogle = window.adsbygoogle || []).push({}); 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]

b)

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fouiers series Calculate sum

**Physics Forums | Science Articles, Homework Help, Discussion**