Find the sum of the following series to n terms:

1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ………

The nth term be


Where = (n - 0) + (n - 1) + (n - 2) + …… + (n - n)




Since,



………(1)


1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ………….=


From (1)


1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ………..


Thus, solving




Solving


We know by property that:


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


Thus,



We know,





Substituting








Thus the answer is


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