Find out if sum_(k=1)^oo((k+1)/(2^k)) converges

Jase Rocha 2022-09-27 Answered
Find out if k = 1 k + 1 2 k converges
I have split it into
k = 1 k + 1 2 k = k = 1 k 2 k + k = 1 1 2 k ,
and applied the geometric series to the second part of the sum. But how do I deal with the first one to find the limit?
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Answers (1)

Dillon Levy
Answered 2022-09-28 Author has 12 answers
Because for all k 10 we have 2 k > k 3 and
k = 10 + 1 k 2
converges.
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