Solve the limit: $ \lim\limits_{n\to\infty}\prod\limits_{1\leq k\leq n}\left( 1+\frac{k}{n} \right)^{\frac{1}{k}} .$
Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$