# Sky is the limit!

Calculus Level 5

$\large \prod_{\alpha = 1}^{99} \lim_{n \to \infty} \prod_{k=1}^{\alpha n} \sqrt [n] {1+\frac nk} = a^b$

The equation above holds true for some positive integers $a$ and $b$. Find the minimum value of $a+b$.

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