1388. Write the first five terms of the series given the general term $a_{n}=\frac{1}{n(n+1)}$.
Solution. Setting $n=1$, we get $a_{1}=\frac{1}{1 \cdot 2}$. If $n=2$, then $a_{2}=\frac{1}{2 \cdot 3}$, if $n=3$, then $a_{3}=\frac{1}{3 \cdot 4}$, and further (for $n=4 ; 5$) $a_{4}=\frac{1}{4 \cdot 5}, a_{5}=\frac{1}{5 \cdot 6}$. Therefore,

$$
\sum_{n=1}^{\infty} \frac{1}{n(n+1)}=\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+\frac{1}{4 \cdot 5}+\frac{1}{5 \cdot 6}+\ldots
$$