2022 TMJC P1 Q1
(i)
Express $\frac{3}{r}+\frac{2}{r+1}-\frac{5}{r+2}$ as a single fraction.
[1]
(ii)
Hence find $\sum\limits_{r=1}^{n}{\frac{4r+3}{r\left( r+1 \right)\left( r+2 \right)}}$.
[3]
(iii)
Use your answer to part (ii) to find $\sum\limits_{r=3}^{n}{\frac{4r-5}{r\left( r-1 \right)\left( r-2 \right)}}$.
[2]
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