Possible Duplicate:
$\lim\limits_{x\to\infty}f(x)^{1/x}$ where $f(x)=\sum\limits_{k=0}^{\infty}\cfrac{x^{a_k}}{a_k!}$.
Suppose $\{a_k\}$ be an strictly increasing sequence with positive integers.
Let $f(x)=\sum_{k=1}^\infty \cfrac{x^{a_k}}{a_k!}$. does $\lim\limits_{x\to +\infty}f(x)^\frac{1}{x}$ exist? and how to compute.