Sum of series n(n+1)(n+5) as a product of linear factors

[MegaDeth]

Homework Statement

(1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5)

Homework Equations

Find an expression for the sum of the series. Give your answer as a product of linear factors in n.

The Attempt at a Solution

I haven't tried it since I don't know what to do.

 

[Delphi51]

I haven't seen one of those for years! They are interesting. There is some theory saying that the sum is equal to a polynomial with one degree higher than the term. Your terms are 3rd degree, so you need a 4th degree polynomial:
S = a*n^4 + b*n^3 + c*n^2 + d*n + e
By hand you figure out the sum and the powers for n = 1, 2, 3, 4, and 5.
That gives you a system of 5 equations with 5 unknowns a, b, c, d, e.
Solve the system to get the unknown coefficients.