级数求和的一个常见错误及解析

A Common Error in Summing a Series

本文针对级数求和问题展开讨论.从一个级数求和的例子出发,列举了两种常见的解题方法,得到了两种不同的结果.问题的根源是函数项级数是否一致收敛.最后本文给出了第三种解法.

This paper discusses the summing of a series.With an example,two approaches are used which lead to two different results.The problem relates to whether or not the uniform convergence holds.Finally,a third approach is presented.