2022 YIJC Promo Q4
(a)
Express $\frac{5r+8}{r\left( r+1 \right)\left( r+2 \right)}$ in partial fractions.
[2]
(b)
Hence, find $\sum\limits_{r=\,\,1}^{n}{\frac{5r+8}{r\left( r+1 \right)\left( r+2 \right)}}$, giving your answer in the form $M-\frac{P}{n+1}-\frac{Q}{n+2}$, where $M$, $P$ and $Q$ are constants to be determined.
[3]
(c)
Use your answer in part (b) to find $\sum\limits_{r=\,\,11}^{n+1}{\frac{5r+3}{r\left( {{r}^{2}}-1 \right)}}$.
[3]
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