# Go Uniformly

Calculus Level pending

If the sequence of the function $\displaystyle f_{n}(x)={(1-x^k)^n}$ where $n,k\in\mathbb {N}$, then find the value of $\lim_{M\to\infty}\lim_{n\to\infty}\sum_{N=1}^{M}\left(\sum_{m=1}^N\sum_{k=1}^m\sqrt[n]{\int_0^1f_n(x)dx}\frac{1}{m^2}+\ln \left(\frac{1}{N+1}\right)\right)\frac{e}{M}.$ Here $e$ is Euler's number.

Motivated by Is it $1^{\infty}$? and main posting of the problem is here.

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