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## Homework Statement

Determine whether [tex]\sum\frac{1}{(2^{n}-n)}[/tex] from n=1 to infinity converges or diverges.

## Homework Equations

a[tex]_{n}[/tex] converges if [tex]\stackrel{lim}{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_{n}}\right|<1[/tex].

## The Attempt at a Solution

I'm really having a tough time knowing where to start on this one. I've tried the integral test, the comparison test, and the ratio test with no luck. Wolfram Alpha says it converges by the ratio test, but I know of no way to simplify [tex]\stackrel{lim}{n\rightarrow\infty}\left|\frac{2^{n}-n}{2^{n+1}-n-1}\right|[/tex]. Is it possible to just say this converges, or is there a mathematical trick to simplifying the ratio? Thanks in advance for the help!