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