im having a hard time computing the following series:
$ \sum_{n=-\infty}^\infty f_n e^{in\theta}$
where $f_n=\alpha^n$, $f_n=f^*_{-n}$, $|\alpha|\leq 1$ is complex number and $f_0$ =1 . I can Splitt the series
$ \sum_{n=-\infty}^{-1} (\alpha^*)^n e^{in\theta} + \sum_{n=1}^\infty \alpha^n e^{in\theta} $
Im pretty sure that i need to use the geometrical series but i dont now what to do with $e^{in\theta} $