Infinite product

Calculus Level 5

\[ \large r = \lim_{n\to\infty} \sqrt[n]{1 + \dfrac{n^2}{(n+1)^2}} \cdot \sqrt[n]{1 + \dfrac{n^2}{(n+2)^2}} \cdots \sqrt[n]{1 + \dfrac{n^2}{(n+n^4)^2}} \]

Find the value of the closed form of \(r\) to 3 decimal places.