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prove by induction, for all n less than equal to 1:

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Trivial:

For n=1: 0 = 0

 

For n+1: (n+1)n + (n-1)n(n+1)/3 = n(n+1)(3 + n-1)/3 = n(n+1)(n+2)/3

 

The original question should be for all n > 0.

Edited by mathematic

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