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

Joel French 2022-07-13 Answered
Convergence of a n n given that a n 2 converges
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Answers (1)

Dayana Zuniga
Answered 2022-07-14 Author has 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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