Question

The value of $1000\left[\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+......+\frac{1}{999\times 1000}\right]$ is equal to

• A. 1000
• B. 999
• C. 1001
• D. 1/999

Answer 1

Answer: (B)

$1000\left[\frac{1}{1\times 2}\times \frac{1}{2\times 3}+\frac{1}{3\times 4}+\dots +\frac{1}{999\times 1000}\right]$
$=1000\{\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)$
$+\dots +\left(\frac{1}{999}-\frac{1}{1000}\right)]$
$=1000\left(1-\frac{1}{1000}\right)$
$=1000\times \frac{999}{1000}$
$=999$