Find the sum of the following series to n terms:

3 × 12 + 5 × 22 + 7 × 32 + …………..

The nth term will be n2×(2n + 1)


The generalized equation be



We know by property that:


∑axn + bxn - 1 + cxn - 2…….d0=a∑xn + b∑xn - 1 + c∑xn - 2…….. + d0∑1


Thus


………(1)


We know






Substituting the values in (1)


=


=


=


=


7