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## Homework Statement

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

## Homework Equations

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

## 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.

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