[ 1 2 ] + [ 1 2 + 1 100 ] + [ 1 2 + 2 100 ] + .... + [ 1 2 + 99 1… - Vidyadip

MCQ

$\left[ {\frac{1}{2}} \right] + \left[ {\frac{1}{2} + \frac{1}{{100}}} \right] + \left[ {\frac{1}{2} + \frac{2}{{100}}} \right] + .... + \left[ {\frac{1}{2} + \frac{{99}}{{100}}} \right] =\ . . . . \ ($કે જ્યાં $[x]$ એ મહતમ પૃણાંક વિધેય છે$)$

A
$49$
✓
$50$
C
$48$
D
$51$

✓

Answer

Correct option: B.

$50$

$\because$ $[x]$ denotes the integral part of $x$.
Hence, after term $\left[ {\frac{1}{2} + \frac{{50}}{{100}}} \right]\,,$ each term will be one.
Hence the sum of given series will be $50.$

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