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)






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