I get the process for this, but not the point

I mean,

To prove that sigma(1 to n) {r(r+1)(r+2)} = (1/4)n(n+1)(n+2)(n+3)

Consider n = k+1

sigma(1 to k+1) {r(r+1)(r+2)} = sigma(1 to k) {r(r+1)(r+2)} + (k+1)(k+2)(k+3)

= (1/4)(k+1)(k+2)(k+3)(k+4)

True for n = k + 1, so true for all n is a member of Z+.

It's the last bit I don't get