调和级数案例教学

由一个数学问题引出了调和级数,并通过对调和级数的敛散性的研究,讲授了级数收敛的定义,子列收敛定理、正项级数收敛的判断准则、单调有界原理以及欧拉常数等高数知识,最后介绍了如何利用欧拉常数计算一些数列的极限值.

A Case Teaching of Harmonic Series

After the discussion of the convergence of harmonic series introduced by a mathematic problem ,some knowledge of higher mathematics as the definition of convergence of series ,the theorem of subsequ - ence conver-gence ,the judging standards of the convergence series of positive terms ,the principle of monotone bounded and Euler’s constant were given to students .At last ,the calculation of the sequence limit of Euler’s constant was in-troduced .