Question 87
Evaluate the limit
$$
\lim_{n \rightarrow \infty} n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\left(1^{1} \cdot 2^{2} \cdots n^{n}\right)^{\frac{1}{n^{2}}}.
$$
$$
\lim_{n \rightarrow \infty} n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\left(1^{1} \cdot 2^{2} \cdots n^{n}\right)^{\frac{1}{n^{2}}}.
$$