Finding C for a PMF of a frequency distribution

N has probability mass function: $p_o = p_1 =0$ and $p_k = c/k!$ for $k=2,3,4,…$ I used exp series $sum_{n=1}^{infty} frac{x^k}{k!} = e^x$ to get $ csum_{n=1}^{infty} frac{1}{k!}$ then $ce=1$ to get $c = 1/e$ Did I do something wrong?