Evaluation of sum_(n=1)^infty (2n-1)/2^n

kemecryncqe9

kemecryncqe9

Answered question

2022-11-07

Evaluation of n = 1 2 n 1 2 n

Answer & Explanation

iletsa2ym

iletsa2ym

Beginner2022-11-08Added 22 answers

Note that
2 n 1 2 n = n 2 n 1 1 2 n
Now make use of the following. For | x | < 1, we have
n = 0 x n = 1 1 x
Differentiating both sides, we get that
n = 0 n x n 1 = 1 ( 1 x ) 2
Take x=1/2 to get what you want.

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