Solution
= Solution
The inequality $(1+1/n)^n\leq e$ gives, for $|x|<1$,
$$
\sum_{n=1}^\infty |x|^n\left(1+\frac1n\right)^n
\leq e\sum_{n=1}^\infty|x|^n<\infty.
$$
For $|x|>1$, the terms have magnitude at least $|x|^n$ and therefore do not tend to zero, so the series diverges by the <term test for divergence>. Hence
$$
\boxed{R=1}.
$$