Infinite product

Calculus Level 4

r=limn1+n2(n+1)2n1+n2(n+2)2n1+n2(n+n4)2n \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 rr to 3 decimal places.

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