Question

The value of $100[\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}]$.

• A. is an integer.
• B. lies between $50$ and $98.$
• C. is $100$
• D. $99$

Answer 1

Answer: (A), (D)

The correct options are
A is an integer.
D $99$

The given series can be written as $100[\frac{2-1}{1.2}+\frac{3-2}{2.3}+.....+\frac{100-99}{99.100}]$
$=100\left[\right(\frac{1}{1}-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+.....+(\frac{1}{99}-\frac{1}{100}\left)\right]$
$=99$