Question

$\frac{1}{2\times4}+\frac{1}{4\times6}+\frac{1}{6\times8}+.....+\frac{1}{98\times100}=?$

• A. 49/200
• B. 49/100
• C. 49/101
• D. 49/201

Answer 1

Answer:

A. 49/200

• $\frac{1}{4\times6} = \frac{1}{2} \left( \frac{1}{4} - \frac{1}{6} \right)$

• $\frac{1}{6\times8} = \frac{1}{2} \left( \frac{1}{6} - \frac{1}{8} \right)$

• ...

• $\frac{1}{98\times100} = \frac{1}{2} \left( \frac{1}{98} - \frac{1}{100} \right)$

$[( \frac{1}{4} - \frac{1}{6} ) + ( \frac{1}{6} - \frac{1}{8}) + ..... + ( \frac{1}{98} - \frac{1}{100})]$

$=[\frac14-\frac{1}{100}]$

$=\frac{100-4}{400}$

$=\frac{98}{400}$

$=\frac{49}{200}$