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## Homework Statement

Prove by induction, that for all integer n where n>= 1

[tex] \sum_{i=1}^{n} i(i+1)(i+2) = \frac{n(n+1)(n+2)(n+3)}{4} [/tex]

## Homework Equations

## The Attempt at a Solution

First question is do I start at i=0 or i=1? It says >=, so not sure.

Ok then I added (n+1)(n+2)(n+3) to the right to balance out the n+1 on the left. But what do I do after that. Just simplify? Or am I missing something

[tex] \sum_{i=1}^{n+1} i(i+1)(i+2) = \frac{n(n+1)(n+2)(n+3)}{4}+(n+1)(n+2)(n+3) [/tex]