Convergence of &#x2211;<!-- ∑ --> a n </msub> <msqrt> n </m

Joel French

Joel French

Answered question

2022-07-13

Convergence of a n n given that a n 2 converges

Answer & Explanation

Dayana Zuniga

Dayana Zuniga

Beginner2022-07-14Added 16 answers

Let a n = 1 n log n . Then n = 2 a n 2 = n = 2 1 n log 2 n which converges by Cauchy's condensation test, but
n = 2 a n n = n = 2 1 n log n
and this diverges, again by Cauchy's condensation test.

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