Find the sum of the following series to n terms:
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ………….
The last term be n(n + 1)
The generalized equation be
……………….(1)
Since We know by property that:
∑axn + bxn - 1 + cxn - 2…….d0=a∑xn + b∑xn - 1 + c∑xn - 2…….. + d0∑1
We know
Thus substituting in (1)