# Can somebody show me how to go from one expression to the other?

• Nov 7th 2012, 06:03 AM
MathIsOhSoHard
Can somebody show me how to go from one expression to the other?
I have the following expression:
$-\frac{1}{4}\cdot\frac{(-2+n\cdot sin(\pi n)\pi + 2cos(\pi n))\cdot sin(nx)}{n^3}$

I need to rewrite it and end up with:
$\frac{sin((2n-1)t)}{(2n-1)^3}$
• Nov 7th 2012, 02:53 PM
richard1234
Re: Can somebody show me how to go from one expression to the other?
What is t? Or should it be $\pi$?
• Nov 7th 2012, 03:03 PM
MathIsOhSoHard
Re: Can somebody show me how to go from one expression to the other?
Quote:

Originally Posted by richard1234
What is t? Or should it be $\pi$?

Nevermind, I figured it out on my own. :)
It's part of a fourier series. I found out that for all $n=even$ the expression will yield zero and for all $n=uneven$ the expression will yield $\frac{sin(nt)}{n^3}$

For $n$ expressed as an uneven integer, we can rewrite it as $n=2k-1$ thus if you insert this and change $k$ to $n$ in the new expression, the work is then complete. :) Sorry for not writtign my question that good, my bad.