$10 \cdot 61$ The algebraic expression $\frac{1}{\log _{2} 100!}+\frac{1}{\log _{3} 100!}+\frac{1}{\log _{4} 100!}+\cdots+\frac{1}{\log _{100} 100!}$ has the value
(A) 0.01 .
(B) 0.1 .
(C) 1 .
(D) 2 .
(E) 0 .
(49th American High School Mathematics Examination, 1998)
[Solution] By the properties of logarithms, we have
$$
\begin{aligned}
\text { Original expression } & =\log _{100!} 2+\log _{100!} 3+\cdots+\log _{100!} 100 \\
& =\log _{100!} 100! \\
& =1
\end{aligned}
$$

Therefore, the correct choice is (C).