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- #1

$$

a^n-b^n = (a-b)\sum\limits_{k = 0}^{n-1}a^kb^{n-k-1}.

$$

To show this is it best to just divide $a^n-b^n$ by $a-b$, show that polynomial is the summation, and then show that $(a-b)$ times the sum is $a^n-b^n$?

Or is there a more efficient method?