已知数列 $\left\{a_n\right\}$ 满足 $a_1=1, a_{n+1}=$ $\frac{a_n}{1+\sqrt{a_n}}\left(n \in \mathbf{N}^*\right)$. 记数列 $\left\{a_n\right\}$ 的前 $n$ 项和为 $S_n$, 则
$\text{A.}$ $\frac{3}{2} < S_{100} < 3$
$\text{B.}$ $3 < S_{100} < 4$
$\text{C.}$ $4 < S_{100} < \frac{9}{2}$
$\text{D.}$ $\frac{9}{2} < S_{100} < 5$