Let $\displaystyle \sum_{n=1}^\infty z_n$ be a series of complex numbers.. Show that if $\displaystyle \lim_{n \to \infty}|\frac{z_{n+1}}{z_n}|=L<1$ then there exists N such that for all positive integers k: $\displaystyle |z_{N+k}|\leq|z_N|(\frac{L+1}{2})^k$.

My first thoughts were to find a specific epsilon in terms of L and N to make the equation, but I couldn't find any. Could someone point me in the right direction?