- #1

ehrenfest

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**[SOLVED] convergence of a series**

## Homework Statement

Prove that the convergence of [itex]\sum a_n[/itex] implies the convergence of [itex]\sum \frac{a_n}{n}[/itex] if [itex]a_n \geq 0[/itex].

## Homework Equations

## The Attempt at a Solution

I want to use the comparison test. So, I want to find [itex]N_0[/itex] so that [itex]n \geq N_0[/itex] implies [tex]\frac{\sqrt{a_n}}{n} \leq a_n[/tex] which is clearly not in general possible. So I am stuck. Maybe I need to replace a_n by a subsequence of a_n or something?