Sum[((-1)^k (2 k)!)/((2 k + 3 n)! 3^k), {k, 0, Infinity}] == Sum[-(((-8)^j (7 - 9 n + 9 j))/((1 - n + j) (2 - 3 n + 3 j) (3 n - 1)!)), {j, 0, n - 2}] - (((-1)^n 2^(-2 + 3 n)) (-(Pi/(2 Sqrt[3])) + (3/2) (1 + Log[3] - Log[4])))/(3 n - 1)! /; Element[n, Integers] && n > 0

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Troy Kessler

2007-05-02