一类等比级数在幂级数问题中的应用

Applications of Geometric Series to Power Series

幂级数是函数级数中的一类重要级数。对于幂级数,主要讨论两方面的问题:一方面是收敛性及和函数问题;另一方面是如何将已知函数展开成幂级数。就此讨论一类等比级数在求幂级数的和函数以及将函数展开成幂级数时的应用。

Power series is a kind of very important function series. For power series, there are two basic problems： one is convergence and sum; the other is representation of functions by power series. In this paper, we discuss how to use the geometric series to find the sums of power series and to represent functions by power series.