Question

The value of $1000\left[\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...... +\frac{1}{999\times1000}\right]$ is equal to

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

Answer 1

Answer: (B)

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