$10 \cdot 78$ If the first term of an infinite geometric series is a positive integer, the common ratio is the reciprocal of a positive integer, and the sum of the series is 3, then the sum of the first two terms of the series is
(A) $\frac{1}{3}$.
(B) $\frac{2}{3}$.
(C) $\frac{8}{3}$.
(D) 2 .
(E) $\frac{9}{2}$.
(26th American High School Mathematics Examination, 1975)
[Solution] If $a$ is the first term of this sequence, and $\frac{1}{n}$ is its common ratio, then we have
$$
\frac{a}{1-\frac{1}{n}}=3 \text { or } a=3-\frac{3}{n} \text {. }
$$

Since $a$ and $n$ are integers, and $0<\frac{1}{n}<1$, hence $n=3, a=2$. $\therefore$ The sum of the first two terms of the sequence is $2+2 \cdot \frac{1}{3}=\frac{8}{3}$. Therefore, the answer is $(C)$.