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

Question

Express $\frac{1}{\left( x+1 \right)\left( x+2 \right)}$ in partial fractions. Hence, Evaluate $\frac{1}{\left( 2 \right)\left( 3 \right)}+\frac{1}{\left( 3 \right)\left( 4 \right)}+\frac{1}{\left( 4 \right)\left( 5 \right)}+...+\frac{1}{\left( 19 \right)\left( 20 \right)}$. Find the value of $n$ if $\frac{1}{\left( 2 \right)\left( 3 \right)}+\frac{1}{\left( 3 \right)\left( 4 \right)}+\frac{1}{\left( 4 \right)\left( 5 \right)}+...+\frac{1}{\left( n-1 \right)\left( n \right)}=\frac{49}{100}$.

Accepted Answer

$\frac{1}{x+1} - \frac{1}{x+2}$ (i) $ \frac{9}{20}$ (ii) $n = 100$

Polynomials, Cubic Equations and Partial Fractions - Higher Order Thinking Questions

Polynomials, Cubic Equations and Partial Fractions - Higher Order Thinking Questions

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