I have to prove, using mathematical induction, that:(adsbygoogle = window.adsbygoogle || []).push({});

n^3 - n is divisible by 6.

When n = 1 its true.

Assuming that k^3 - k is divisible by 6

(k+1)^3 - (k+1)

=k^3 + 3k^2 + 2k

= k^3 - k + 3k^2 + 3k

k^3 - k is true by induction hypothesis

but how would i prove that 3k^2 + 3k is divisible by 6? (or did i do this completely wrong?)

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# Proof by Induction

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