Factorials

Calculus Level pending

\({\bf \sum_{J = 2}^{1001} ((\frac{2001}{2})! + J) = }\) \({\bf a + \frac{b!\sqrt{\pi}}{2^b * c!} }\), where \({\bf b > c }\) and \({\bf gcf(a,b,c) = 1 }\).

Find: \({\bf a + b + c. }\)

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