I need to find the residue of(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{e^{2/z}}{1+e^z}

[/tex]

at z = [itex]\pi i[/itex]

I've been scribbling over numerous papers trying to figure this out. So far I've tried to expand the denominator

[tex]

\frac{e^{2/z}}{(1-e^z + \frac{e^{2z}}{2!} - ...)}

[/tex]

I think maybe I've expanded that incorrectly, but I was thinking about pulling an [itex]e^z[/itex] out of the denom and multiplying the entire function [itex]f(z)[/itex] by the expanded 'leftovers', but I think that's incorrect too..

[tex]

\frac{e^{2/z}}{e^z(\frac{1}{e^z}-1+1-...)}

[/tex]

I feel like my steps are misguided because I can't seem to see where to go next.

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# Homework Help: Need to find the residue

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