2. Given the sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ satisfy:
$$
a_{k} b_{k}=1(k=1,2, \cdots) \text {, }
$$

the sum of the first $n$ terms of the sequence $\left\{a_{n}\right\}$ is $A_{n}=\frac{n}{n+1}$. Then the sum of the first $n$ terms of the sequence $\left\{b_{n}\right\}$ $B_{n}=$ . $\qquad$
2. $\frac{n(n+1)(n+2)}{3}$.

Notice that
$$
\begin{array}{l}
a_{1}=A_{1}=\frac{1}{2}, \\
a_{n}=A_{n}-A_{n-1}=\frac{1}{n(n+1)}, \\
b_{n}=\frac{1}{a_{n}}=n(n+1) .
\end{array}
$$

Thus, $B_{n}=\sum_{k=1}^{n}\left(k^{2}+k\right)=\frac{n(n+1)(n+2)}{3}$.