We need to find the sum of n terms of series whose r^th term is r + 2^r.

a_r = r + 2^r

So, n^th term, a_n = n + 2ⁿ

So, we can find the sum of the series by using summation of the n^th term of the given series.

→ (1)

Note:

I. Sum of first n natural numbers, 1 + 2 +3+…n,

Second term in (2) is a GP, with first term a = 2, common ratio r = 2.

Sum of n terms of GP, with the first term, a, common ratio, r,

So, the sum of given GP, with a = 2, r = 2

The required sum,

The sum of n terms of the series whose r^th term is (r + 2^r),