Determine the coefficient $a_{-4}$ in the Laurent expansion in the region $0<|z|<1$ of the function $f(z)=\frac{e^{1/z}}{1-z}$
I'm new using Laurent series so all help is appreciated.
My first thought was to write
$f(z)=\frac{e^{1/z}}{1-z}=\sum_{j=0}^\infty\frac{1}{n!z^n}\cdot \sum_{n=0}^\infty z^n$,
and continue from there.
Is this correct what to go? Or should i calculate otherwise?