交错二项式系数连带奇数倒数平方和级数

The Series of Binomial Coefficients Associated Square Sum of Reciprocal of Continuative Odd Numbers

根据一个已知级数,使用裂项方法得到一个分母含有1个、2个、3个等奇偶性因子的二项式系数连带奇数倒数平方和的级数。利用反正弦与反双曲正弦关系给出交错二项式系数倒数连带连续奇数倒数平方和级数。得到级数封闭型的和式,同时得到二项式系数连带奇数倒数平方和的级数恒等式。

According to a known series,Msing the split term method to get a series with 1,2,and 3 equal parity factors of the denominator and the odd reciprocal square sum of the binomial coefficient.By the relation between arcsine and inverse hyperbolic function,the reciprocal series of alternating binomial coefficient with continuous odd reciprocal square sum was given.The closed summation of the series was obtained,and the series identity of the binomial coefficient with the odd reciprocal square summation was obtained.