Ononot — A sequence an satisfies a{n+1} = an \cdot rn where rn = \fra

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Geometric Sequenceshard

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A sequence $a_n$ satisfies $a_{n+1} = a_n \cdot r_n$ where $r_n = \frac{n+2}{n}$ . Given $a_1 = 1$ , find the closed-form expression for $a_n$ and determine if the series $\sum_{n=1}^{\infty} \frac{1}{a_n}$ converges.