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## Homework Statement

[tex]\sum^{\infty}_{n=1} \frac{n}{2^{n}}[/tex]

Does this series converge or diverge?

## Homework Equations

## The Attempt at a Solution

By the Cauchy condensation test (http://en.wikipedia.org/wiki/Cauchy_condensation_test) I think this one diverges. But not sure if I am using it correctly.

According to the test,

[tex]\sum^{\infty}_{n=1} \frac{n}{2^{n}}[/tex]

converges if and only if

[tex]\sum^{\infty}_{n=1} 2^{n} \frac{2^{n}}{2^{n}} = \sum^{\infty}_{n=1} 2^{n}[/tex]

converges, which doesn't.

Thank you for any help.