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

[pankajkumar]

sigma i=1 upto n, i(i-1)= n(n-1)(n+1)/3

[mathematic]

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 May 16, 2013 by mathematic