Answer :

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 + 2^{n}

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}),

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