(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\sum_{x=1}^{\infty}\left({e^{{x}^{-1}}}-1\right)[/tex]

Test for convergence/divergence

3. The attempt at a solution

Using the Taylor expansion of e^x, we have...

[tex]1+ \frac{1}{x} + \frac{1}{2!*x^2} + \frac{1}{3!*x^3} + ...[/tex]

So as n -> infinity, we see that the function tends to [tex]1+ \frac{1}{x}[/tex]. Now we subtract 1 from this. So apparently the sum seems to act as according to the harmonic series, so it should be divergent. Is my reasoning correct? I tried solving it on maple, which refused to give a solution (perhaps since it was divergent).

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# Easy series divergence/convergence problem

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