Let $\displaystyle {a}_{n}\geq 0$. Prove that if $\displaystyle \sum {a}_{n}$ converges, then $\displaystyle \sum \frac{\sqrt{{a}_{n}}}{n}$ converges.
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Use the Cauchy–Schwarz inequality on the series $\displaystyle \sum \sqrt{a_n}$ and $\displaystyle \sum \frac1n$.
thanks. That does it.
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