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?
Convergence test for positive series
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calculus
real-analysis
sequences-and-series
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0What do you mean by "$<\infty$"? – 2012-10-09
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1@Jacob That it converges to a finite number. – 2012-10-09
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0I mean less than infinity or what is the same that the series converge – 2012-10-09