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
A
$\frac{3}{2} < S_{100} < 3$
B
$3 < S_{100} < 4$
C
$4 < S_{100} < \frac{9}{2}$
D
$\frac{9}{2} < S_{100} < 5$
E
F