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

Question

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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have, [(1/2)]+[(1/2) + (1/100)]+[(1/2) + (2/100)]+ ldots .+[(1/2) + (99/100)] =0+0+...+[(1/2) + (50/100)]+[(1/2) + (51/100)]+...+[(1/2) + (99/100)] =1+1+...+1 =50

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

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

Q. If [.] denotes the greatest integer function, then the value of [21​]+[21​+1001​]+[21​+1002​]+ ….+[21​+10099​] is

We have, [21​]+[21​+1001​]+[21​+1002​]+….+[21​+10099​] =0+0+...+[21​+10050​]+[21​+10051​]+...+[21​+10099​] =1+1+...+1 =50

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

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