Find the closed form sum of 1*2*3 + 2*3*4 + 3*4*5 + ... + n(n + 1)(n + 2).
n∑k=1(k)(k+1)(k+2) .
The "closed form" of the sequence is:
a_n = n^3 + 3 n^2 + 2 n
Not exactly a derivation, but
It can be proved by induction.
