Find the sum of n

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

ar = r + 2r

So, nth term, an = n + 2n

So, we can find the sum of the series by using summation of the nth 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 rth term is (r + 2r),

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