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 + bx^{n - 1} + cx^{n - 2}…….d₀=a∑xⁿ + b∑x^{n - 1} + c∑x^{n - 2}…….. + d₀∑1

Thus,

We know,

Substituting

Thus the answer is