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　数列$\{a_n\}$を
\[ a_1=\frac{1}{3}, \hspace{1zw} \frac{1}{a_{n+1}}-\frac{1}{a_n}=1 \hspace{1zw}
(n=1, \, 2, \, 3, \, \cdots\cdots) \]
で定め，数列$\{b_n\}$を
\[ b_1=a_1a_2, \hspace{1zw} b_{n+1}-b_n=a_{n+1}a_{n+2} \hspace{1zw}
(n=1, \, 2, \, 3, \, \cdots\cdots) \]
で定める．
\begin{description}
\item[(1)]一般項$a_n$を$n$を用いて表せ．
\item[(2)]一般項$b_n$を$n$を用いて表せ．
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