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  4. If [.] denotes the greatest integer function, then the value of [(1/2)]+[(1/2) + (1/100)]+[(1/2) + (2/100)]+ ldots .+[(1/2) + (99/100)] is

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Q. If $\left[.\right]$ denotes the greatest integer function, then the value of $\left[\frac{1}{2}\right]+\left[\frac{1}{2} + \frac{1}{100}\right]+\left[\frac{1}{2} + \frac{2}{100}\right]+$ $\ldots .+\left[\frac{1}{2} + \frac{99}{100}\right]$ is

NTA AbhyasNTA Abhyas 2022

Solution:

We have, $\left[\frac{1}{2}\right]+\left[\frac{1}{2} + \frac{1}{100}\right]+\left[\frac{1}{2} + \frac{2}{100}\right]+\ldots .+\left[\frac{1}{2} + \frac{99}{100}\right]$
$=0+0+...+\left[\frac{1}{2} + \frac{50}{100}\right]+\left[\frac{1}{2} + \frac{51}{100}\right]+...+\left[\frac{1}{2} + \frac{99}{100}\right]$
$=1+1+...+1$
$=50$