<s>[INST] Question Regarding Telescopic Sums How do I find a formula for the partial sum $s_n$ for the series $$\sum_{k=1}^{\infty}(\frac{1}{k}-\frac{1}{k+2})$$
 [/INST] For example: $$\left(\dfrac{1}{1} - \dfrac{1}{3}\right) + \left(\dfrac{1}{2} - \dfrac{1}{4}\right) + \left(\dfrac{1}{3} - \dfrac{1}{5}\right) = 
\dfrac{1}{1} + \dfrac{1}{2} - \dfrac{1}{4} - \dfrac{1}{5}$$
Try a few more: do you see the pattern?
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