一类双交错级数的收敛性及求和法

The Convergence and Summation of Bi-alternating Series

讨论了双交错级数的收敛性问题 ,利用极限理论证明了双交错级数的收敛性 ,从而推广了判别交错级数收敛性的莱布尼兹法。并对一类特殊的双交错级数求和问题 ,给出了相应的求和公式和示例。

Using the limit theorem,the paper proves the convergence of the bi-alternating series,thus extending Leibniz′s criterion on it.A summation formula is given for a special alternating series and an example presented.