关键词: 留数定理, 无穷项级数求和, 三角函数

Abstract: We discuss the method of summation of some infinite series by the residue theorem,then extend to infinite series containing trigonometric function and give rigorous proofs. Finally,we illustrate the correctness of the present results and compare the result of an example by using two different methods. From an example,we see the effectiveness of residue theorem in the simplification of infinite series.

Key words: residue theorem, sum of infinite series, trigonometric function