一个条件收敛级数重排项后的和

研究了以自然数倒数所构成的一个典型交错级数重排项后所得级数的收敛性及求和问题．证明了当其正项和负项均按由小到大的顺序排列后，每出现r个正项后面接t个负项的排列所得到的级数收敛，并利用幂级数求得了重排项后级数的和．

Sum of a Conditional Convergence Series after Rearranging Terms

We investigate the convergence and the sum of a classical alternate series consisting of reciprocal of natural numbers after rearranging terms. It is proved that after its positive terms and negative terms are arranging from large to small, the obtained series according to permutation of every r positive terms following t negative terms converges. Tha sum of this series is also obtained by using exponential series.