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1.Relation and Function
medium
For a real number $x,\;[x]$ denotes the integral part of $x$. The value of $\left[ {\frac{1}{2}} \right] + \left[ {\frac{1}{2} + \frac{1}{{100}}} \right] + \left[ {\frac{1}{2} + \frac{2}{{100}}} \right] + .... + \left[ {\frac{1}{2} + \frac{{99}}{{100}}} \right]$ is
A
$49$
B
$50$
C
$48$
D
$51$
(IIT-1994)
Solution
(b) $[x]$ 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 $50.$
Standard 12
Mathematics
