$31 \cdot 30$ The positive integer solution to the equation $\frac{1+3+5+\cdots+(2 n-1)}{2+4+6+\cdots+2 n}=\frac{115}{116}$ is
(A) 110.
(B) 115.
(C) 116.
(D) 231.
(E) The equation has no positive integer solution.
(30th American High School Mathematics Examination, 1979)
[Solution] The numerator and denominator of the given expression are both sums of arithmetic sequences, thus
$$
\frac{115}{116}=\frac{1+3+\cdots+(2 n-1)}{2+4+\cdots+2 n}=\frac{n^{2}}{n(n+1)},
$$

which means $\frac{115}{116}=\frac{n}{n+1}$, leading to $n=115$.
Therefore, the answer is $(B)$.