# Math Help - a^n - b^n

1. ## a^n - b^n

Hi im wondering how one can obtain the formula $a^n - b^n = (a-b) \sum_{k=0}^{n-1}a^{n-1-k}b^k$ out of the fact that $(1-x)\sum_{k=0}^{n-1}x^{k}= 1 - x^n$.

I started via $a^n - b^n = 1 -b^n -(1 - a^n) = (1-b)\sum_{k=0}^{n-1}b^{k} - (1-a)\sum_{k=0}^{n-1}a^{k}$ but don't know how to proceed. Any suggestions?

2. ## Re: a^n - b^n

Originally Posted by EinStone
Hi im wondering how one can obtain the formula $a^n - b^n = (a-b) \sum_{k=0}^{n-1}a^{n-1-k}b^k$ out of the fact that $(1-x)\sum_{k=0}^{n-1}x^{k}= 1 - x^n$.
Set x = b / a.

3. ## Re: a^n - b^n

Wow, that was easy, thanks a lot.