Simplification question..

[MarkSA]

Hello,

I have the following sequence inside a summation:

[(-1)^(n-1) * x^n]/[n^3]

If I let x = -1, how does this the above end up becoming -1/n^3? I'm having trouble seeing it.

On the top I would get (-1)^(n-1) * (-1)^(n). I would think this would become: (-1)^(n-1+n) or (-1)^(2n-1)
But how does (-1)^(2n-1) become -1?

Thanks.

 

[pka]

"But how does (-1)^(2n-1) become -1?"
\(\displaystyle (-1)^{2n-1}=-1\) because \(\displaystyle 2n-1\) is an odd number.
What is (-1) raised to an odd power?