Let $(\alpha_n)$ be a sequence of complex numbers such that $ \sum_{n=1}^\infty \frac{\alpha_n}{k^n} = 0 $ for all $k = 1, 2, 3, ...$ Prove that $\alpha_n=0$ for all $n$
As far as a solution goes, really not sure where to start. Any hints would be appreciated. Thanks.