Question

The value $\left[\frac{1}{2}\right]+[\frac{1}{2}+\frac{1}{100}]+[\frac{1}{2}+\frac{2}{100}]+......+[\frac{1}{2}+\frac{99}{100}]$ is

• A. $99.5$
• B. $50$
• C. $51$
• D. $98$

Answer 1

The correct option is A $99.5$

We have,

$\left(\frac{1}{2}\right)+\left(\frac{1}{2}+\frac{1}{100}\right)+\left(\frac{1}{2}+\frac{2}{100}\right)+..........\left(\frac{1}{2}+\frac{99}{100}\right)$
$\Rightarrow \left(\frac{1}{2}+\frac{1}{2}+......100times\right)+\frac{1}{100}\left(1+2+......99\right)$
$\Rightarrow 50+49.5$.............Sum $=\frac{n(n+1)}{2}$
$\Rightarrow 99.5$

Hence,

Option $A$ is a correct answer.