Express $\frac{r+1}{r+2}-\frac{r}{r+1}$ as a single fraction. Hence, find \(\sum\limits_{r=1}^{10}

Question

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.

Accepted Answer

$\dfrac{5}{12} - 2\ln(3628800)$

2012 RVHS P1 Q9 (a)

2012 RVHS P1 Q9 (a)

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