关于sum from n=1 to ∞(1/n^2=π~2/6)的证明及应用  

On the Proof and Application of sum from n=1 to ∞(1/n^2=π~2/6)

作　　者：刘爱春[1] 祁根锁 

机构地区：[1]呼和浩特民族学院数学系,呼和浩特010051

出　　处：《大学数学》2014年第2期102-107,共6页College Mathematics

摘　　要：鉴于欧拉求得的无穷级数∑∞n=11n2收敛于π26的特殊性和重要性,用列举与对比的方法又给出了∑∞n=11n2=π26的若干不同的证明方法及其应用.Considering the special importance of the eqution ∞∑n=1 n^2/1=6/π^2 which is proved first by Euler, this paper will present and introduce several different proofs and applications of ∞∑n=1 n^2/1=6/π^2 by the way of listing and contrast.

关 键 词：逐项积分 傅立叶级数 逐项求和 

分 类 号：O171.1[理学—数学]