📝 题目
4.3.2 求下列级数的收敛域:
(1) $\mathop{\sum }\limits_{{n = 1}}^{\infty }\frac{{\left( -1\right) }^{n - 1}}{{2n} - 1}{\left( \frac{1 - x}{1 + x}\right) }^{n}$ ; (2) $\mathop{\sum }\limits_{{n = 0}}^{\infty }{\left\lbrack x\left( 1 + x\right) \right\rbrack }^{{3}^{n}}$ .
💡 答案与解析
4.3.2 (1) $\displaystyle{0 \leq x < + \infty}$ ; (2) $\left\lbrack {-\frac{\sqrt{5} + 1}{2},\frac{\sqrt{5} - 1}{2}}\right\rbrack$ .