The nth term be n(n + 1)(n + 4)

Thus we can write 1.2.5 + 2.3.6 + 3.4.7 + ……..

The general term would be r(r + 1)(r + 4)

We know by property that:

∑axⁿ + bx^{n - 1} + cx^{n - 2}…….d₀=a∑xⁿ + b∑x^{n - 1} + c∑x^{n - 2}…….. + d₀∑1

Thus,

=……(1)

We know

Substituting in (1)