Does sum_(n=1)^infty q/n((-1)^n+1/n) converges?

Adison Rogers

Adison Rogers

Answered question

2022-11-05

Does n = 1 1 n ( ( 1 ) n + 1 n ) converges?

Answer & Explanation

luthersavage6lm

luthersavage6lm

Beginner2022-11-06Added 22 answers

That is, if you know that
n = 1 a n and n = 1 b n
both converge with sums a and b respectively, then you know that
n = 1 a n + b n
is convergent with sum a+b
You have simply applied this fact to the example where
a n = ( 1 ) n n and b n = 1 n 2 .
As a matter of "logic" I would first note that n = 1 a n converges. Then note that n = 1 b n converges. Then, with the convergence of the two series, you conclude that n = 1 a n + b n is convergent.

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