Express $\frac{1}{\left( 2x+1 \right)\left( 2x+3 \right)}$ in partial fractions. Hence, show that $\

Question

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

Accepted Answer

$$\dfrac{51}{103}$$

JJC P1 Q13

JJC P1 Q13

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