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#### 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.

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

- Thread starter Alexmahone
- Start date

- Thread starter
- #1

- Jan 26, 2012

- 268

Give a counterexample to

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

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

- Jan 30, 2012

- 2,492

Consider $a_n=\frac{1}{n\ln n}$.