Convergence of a series (using the comparation test ?)

Question

I'll be glad to get some help in this one :)

$a_n>0$ i a sequence such that the series $\sum a_n$ converges. Prove that the series $\sum \frac{\sqrt{a_n}}{n}$ converges. I thought of using the comparation test but thats it.

I'm sorry I didn't know how to write the sigma letter for series :/

Thanks

possible duplicate of http://math.stackexchange.com/questions/756510/convergence-of-sum-frac-sqrta-nnp — Fermat, May 08 '14 at 13:41

score 1 · Answer 1 · edited May 15 '14 at 23:31

1

Regard the partial sums as inner products and use the Cauchy-Schwarz inequality.

edited May 15 '14 at 23:31

answered May 08 '14 at 13:40

user131759

21

Convergence of a series (using the comparation test ?)

1 Answers1