Euler恒等式π~2/6=1+1/2~2+1/3~2+…经常由中学教师向学生介绍.这个恒等式的证明通常都用到较深的分析工具,如Bernouli多项式、Fourier级数、函数的Taylor展开式等等.不少学完微积分的大学生对这个恒等式也是知其然而不知其所以然.本文用DeMoivre公式和简单不等式给出这个恒等式一个初等证明. Euler Identity π ~ 2/6 = 1 + 1/2 ~ 2 + 1/3 ~ 2 + ... Often introduced by secondary school teachers to students, proof of this identity often uses deeper analytical tools such as Bernouli polynomials, Fourier Series, Taylor expansion of the function, etc. Many college students who have completed the calculus also know this identity but do not know why. In this paper, an elementary proof of this identity is given by DeMoivre formula and simple inequality.