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)

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.