Convergence (1)

Calculus Level 3

\[\sum_{n=1}^{\infty}{\dfrac{m^n((500n)!)^2}{(1000n)!}}\] If the series above is to converge, we must have \(|m| < a\). If \(a\) is of the form \(s^r\), where \(s\) is a prime number, find \(s+r\).

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