What will be the value of $$\lim_{n\to\infty} ((1+\frac{1}{n^2})(1+\frac{2}{n^2})(1+\frac{3}{n^2})\cdots(1+\frac {n}{n^2}))$$
My attempt was to use binomial expansion i.e. writing $(1+x^n)$ as $(1+nx)$ and the taking log on both sides. After that I tried using the method of integration for series limits but that led to a wrong answer. I am pretty sure the answer will be 'e' raised to the power something but i am not able to make it out.
All help is appreciated.