JJC P1 Q13
(i)
Express $\frac{1}{\left( 2x+1 \right)\left( 2x+3 \right)}$ in partial fractions.
(ii)
Hence, show that $\sum\limits_{r=1}^{n}{\frac{1}{\left( 2r+1 \right)\left( 2r+3 \right)}}=\frac{n}{3\left( 2n+3 \right)}$.
(iii)
Deduce the sum of $\frac{1}{3}+\frac{1}{3\left( 5 \right)}+\frac{1}{5\left( 7 \right)}+…+\frac{1}{101\left( 103 \right)}$ .
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