Gaokao Math Practice Question
已知数列 $\left\{a_{n}\right\}$ 满足 $a_{1}=1, a_{n+1}=\frac{a_{n}}{1+\sqrt{a_{n}}}\left(n \in \mathrm{N}^{*}\right)$. 记数列 $\left\{a_{n}\right\}$ 的前 $n$ 项和为 $S_{n}$, 则 ($\quad$)
- A.$\frac{1}{2}<S_{100}<3$
- B.$3<S_{100}<4$
- C.$4<S_{100}<\frac{9}{2}$
- D.$\frac{9}{2}<S_{100}<5$
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