Suppose that $\{a_n\}$ is a positive series and converges, i.e. $\sum a_n < +\infty$. Prove that $$\sum \f{\sqrt{a_n}}{n} < +\infty.$$ Can not figure it out, click the following [[http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality|Hint]].