Find the sum of n terms of series whose mth term is 2m + 2m

Question

KnowledgeBoat · Accepted Answer

Given, mth term = 2m + 2m 1st term = 21 + 2 × 1 2nd term = 22 + 2 × 2 nth term = 2n + 2 × n Calculating : 21 + 22 + ........ + 2n The above is an G.P. with a = 2 and r = 2. By using formula, Sn = Substitute values, we get: Sn = = 2(2n - 1) Calculating : (1 + 2 + 3 + ..... + n) The above is an A.P. with a = 1 and d = 1. By using formula, Sn = [2a + (n - 1)d] Substitute values, we get: Sn = [2(1) + (n - 1)1] = [2 + n - 1] = (n + 1). Substitute values in (1) we get, Sn = 2(2n - 1) + (n + 1) = 2(2n - 1) + n(n + 1) Hence, Sn = 2(2n - 1) + n(n + 1).

Mathematics

Find the sum of n terms of series whose mth term is 2^m + 2m

G.P.

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