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Give a counterexample

Alexmahone

Active member
Jan 26, 2012
268
Give a counterexample to

$na_n\to 0,\ a_n\ge 0,\ a_n$ decreasing $\implies\sum a_n$ converges.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,488
Consider $a_n=\frac{1}{n\ln n}$.