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Can someone tell me how I could find a formula for the nth partial sum of the series by using it to find the series' sum if the series converges?

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Based on the following definition:

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I would need to know how I could define a and r

Thanks in advance!

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HINT:

$r$th term $=\frac1{(r+1)(r+2)}=\frac{(r+2)-(r+1)}{(r+1)(r+2)}=\frac1{r+1}-\frac1{r+2}$

So, the given series is Telescopic

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