📝 题目
1.3.9 求证: 如下序列的极限存在:
$$ \mathop{\lim }\limits_{{n \rightarrow \infty }}{\left\lbrack \frac{\left( {2n}\right) !!}{\left( {{2n} - 1}\right) !!}\right\rbrack }^{2}\frac{1}{{2n} + 1} $$
💡 答案与解析
1.3.9 $\frac{{x}_{n + 1}}{{x}_{n}} = \frac{{\left( 2n + 2\right) }^{2}}{\left( {{2n} + 1}\right) \left( {{2n} + 3}\right) }$
$$ \Rightarrow \left\{ \begin{array}{l} \frac{{x}_{n + 1}}{{x}_