问题
关于等比级数 $\sum_{n=1}^{\infty}$ $a q^{n-1}$ 的敛散性,以下选项中,正确的是哪个?选项
[A]. $\sum_{n=1}^{\infty}$ $a q^{n-1}$ $\left\{\begin{array}{ll} =\frac{a}{1-q}, & |q| < 1, \\ 发散, & |q| = 1. \end{array}\right.$[B]. $\sum_{n=1}^{\infty}$ $a q^{n-1}$ $\left\{\begin{array}{ll} =\frac{a}{1-q}, & |q| < 1, \\ 发散, & |q| \geq 1. \end{array}\right.$
[C]. $\sum_{n=1}^{\infty}$ $a q^{n-1}$ $\left\{\begin{array}{ll} =\frac{a}{1-q}, & |q| \leq 1, \\ 发散, & |q| \geq 1. \end{array}\right.$
[D]. $\sum_{n=1}^{\infty}$ $a q^{n-1}$ $\left\{\begin{array}{ll} =\frac{a}{1-q}, & |q| < 1, \\ 发散, & |q| > 1. \end{array}\right.$