Express $\frac{1}{(x+1)(x+2)}$ in partial fractions. Hence, Evaluate $\frac{1}{(2)(3)}+\frac{1}{(3)(

Question

Express $\frac{1}{(x+1)(x+2)}$ in partial fractions. Hence, Evaluate $\frac{1}{(2)(3)}+\frac{1}{(3)(4)}+\frac{1}{(4)(5)}+........+\frac{1}{(19)(20)}$. Find the value of $n$ if $\frac{1}{(1)(2)}+\frac{1}{(2)(3)}+\frac{1}{(3)(4)}+........+\frac{1}{(n-1)(n)}=\frac{99}{100}$.

Accepted Answer

(i) $\frac{9}{20}$, (ii) $n = 100$

Question 114081

Question 114081

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