Originally Posted by **AfterShock**

Here is the problem:

"Let S_n stand for the sum of all the products of the integers, taken two at a time, from 1 to n. For example, S_4 means:

S_4 = 1*2 + 1*3 + 1*4 + 2*3 + 2*4 + 3*4

Prove that S_n is given explicitly by:

S_n = [n*(n^2-1)*(3*n+2)]/24".

So, I was thinking this was the perfect candidate for an induction proof. I thought it would be best to derive the formula first:

Derive formula S_(n+1) = S_n + 1(n+1) + 2(n+1) + ... + n(n+1)

= S_n + n(n + 1)^2 / 2

Now what; base case of course works out. How do I work toward the induction assumption.