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- #1
$n\in\mathbb{N}$, prove
$$
a^n-b^n = (a-b)\sum\limits_{k = 0}^{n-1}a^kb^{n-k-1}.
$$
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?
$$
a^n-b^n = (a-b)\sum\limits_{k = 0}^{n-1}a^kb^{n-k-1}.
$$
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?