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Let $a_n>0$ for all $n\in\mathbb{N}$ and the series $\sum\limits_{n=1}^\infty (n+1) a_n^2$ converges. Does it imply the series $$ \sum\limits_{n=1}^\infty a_n $$ is also converges?

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    What do you mean by "$<\infty$"?2012-10-09
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    @Jacob That it converges to a finite number.2012-10-09
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    I mean less than infinity or what is the same that the series converge2012-10-09

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