Infinite Sequences and Series · Superchallenge problem

Let $a_n=\left(1+\dfrac1n\right)^{n^2}$, and let $R$ be the radius of convergence of the power series $\displaystyle\sum_{n=1}^{\infty}a_nx^n$. Find $\displaystyle\lim_{n\to\infty}a_nR^n$.