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

• Nov 7th 2012, 05:03 AM
MathIsOhSoHard
Can somebody show me how to go from one expression to the other?
I have the following expression:
$\displaystyle -\frac{1}{4}\cdot\frac{(-2+n\cdot sin(\pi n)\pi + 2cos(\pi n))\cdot sin(nx)}{n^3}$

I need to rewrite it and end up with:
$\displaystyle \frac{sin((2n-1)t)}{(2n-1)^3}$
• Nov 7th 2012, 01:53 PM
richard1234
Re: Can somebody show me how to go from one expression to the other?
What is t? Or should it be $\displaystyle \pi$?
• Nov 7th 2012, 02:03 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 $\displaystyle \pi$?

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

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