Limits and Continuity · Superchallenge problem

Find $\displaystyle\lim_{n\to\infty}\prod_{k=1}^{n}\left(1+\dfrac{k}{n^2}\right)=\lim_{n\to\infty}\left(1+\dfrac{1}{n^2}\right)\left(1+\dfrac{2}{n^2}\right)\cdots\left(1+\dfrac{n}{n^2}\right)$.