2012 RVHS P1 Q9 (a)

Express \(\frac{r+1}{r+2}-\frac{r}{r+1}\) as a single fraction.

Hence, find \(\sum\limits_{r=1}^{10}{\left( \frac{1}{{{r}^{2}}+3r+2}-\ln {{r}^{2}} \right)}\)in the form \(\frac{p}{q}-2\ln k\) where \(p\),\(q\) and \(k\) are integers.