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**Ramin_Shahab** Problem :

Prove that for every positive integer n,

1 * 2 * 3 + 2 * 3 * 4 + . . . . . + n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4

Question :

Basis Step:

I want to prove this by determining if P(0) is true which in this case 0(0+1)(0+2)(0+3) = 0 .

Induction Step:

1 * 2 * 3 + 2 * 3 * 4 + . . . . . + k(k+1)(k+2) + (2k+1) =

[k(k+1)(k+2)(k+3)/4 + (2k+1)]

When I simplify I cannot come up with the original solution n(n+1)(n+2)(n+3)/4. I believe I am doing something wrong trying to prove the induction. Any help is appreciated!