3. The sequence $\left\{\frac{100^{n}}{n!}\right\}(n=1,2,3, \cdots)$ is ).
(A) an increasing sequence. (B) a decreasing sequence.
(C) a sequence that has both increasing and decreasing terms after the 1993rd term.
(D) a sequence for which there exists a term such that after this term, it is decreasing.
3. (D).
$$
a_{n}=\frac{100^{n}}{n!}, a_{n-1}=\frac{100^{n-1}}{(n+1)!} .
$$
$\left\{a_{n}\right\}$ is decreasing $\Leftrightarrow \frac{a_{n+1}}{a_{n}} < 1$.

\begin{aligned}
\frac{a_{n+1}}{a_{n}} &=\frac{\frac{100^{n+1}}{(n+1)!}}{\frac{100^{n}}{n!}} \\
&=\frac{100}{n+1} \\
&<1 \Leftrightarrow n+1>100 \Leftrightarrow n>99 .
\end{aligned}
$$

That is, from the 99th term, $\left\{a_{n}\right\}$ is decreasing.