sum from n=1 to +∞(1/n^(2m))的初等解法

Elementary Evaluation of sum n=1 to ∞ n2k/1

本文用初等的方法研究sum from n=1 to(1/n^(2m))(m∈N)的求和问题。这个问题最先由Euler[8]解决。文献[1][6]给出了另两种求解方法。特别地,对于m=1的情形,即sum from n=1 to ∞(1/n^2)=((π~2)/6),已有许多不同的证明方法,可见文献[2][3][4][5]以及那里的参考文献。本文的想法,主要受文献[5][6]的启发而来的。

In this paper we study the sum of the series ,elementary evaluation of it. The sum of this series was first obtained by Euler [8]. [1] [6] give another two solutions. Especiallywhen , there are many proofs, see [2] [3] [4] [5]. This paper is mainly motivated by [5].