摘要： Values of new series ∞ ∑n=1(2n- 1)!ζ(2n)/(2n + 2k)! α2n, ∞∑n=1 (2n- 1)!ζ(2n)/(2n+ 2k + 1)!β2nare given concerning ζ(2k+ 1), where k is a positive integer, α can be taken as 1, 1/2,...
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Values of new series ∞ ∑n=1(2n- 1)!ζ(2n)/(2n + 2k)! α2n, ∞∑n=1 (2n- 1)!ζ(2n)/(2n+ 2k + 1)!β2nare given concerning ζ(2k+ 1), where k is a positive integer, α can be taken as 1, 1/2, 1/3, 2/3,1/4, 3/4, 1/6, 5/6 and β can be taken as 1, 1/2. Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3, or α = 1/4, or α= 1/6.
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