Question

For a real number x, x denotes the integral part of x . The value of 1/2+(1/2+1/100)+(1/2+2/100)+.....+(1/2+99/100) is

Answer 1

Please see the attachment

Answer 2

Concept Introduction:-

Real numbers may be explained because the union of each rational as well as irrational numbers.

Given Information:-

We have been given that $1/2+(1/2+1/100)+(1/2+2/100)+.....+(1/2+99/100)$

To Find:-

We have to find that the value of $1/2+(1/2+1/100)+(1/2+2/100)+.....+(1/2+99/100)$

Solution:-

According to the problem

$=\left[\frac{1}{2}\right]+\left[\frac{1}{2}+\frac{1}{100}\right]+\left[\frac{1}{2}+\frac{2}{100}\right]+\ldots \ldots \ldots \ldots \ldots \ldots .+\left[\frac{1}{2}+\frac{99}{100}\right]$

till $\left[\frac{1}{2}+\frac{49}{100}\right]$ all terms will be zero and after this till $\left[\frac{1}{2}+\frac{99}{100}\right]$ all terms will be $1$.

$\begin{aligned}&=0+0+0+0+0 \ldots \ldots \ldots+1+1+1+\ldots \ldots . .1 \\&=50(0)+50(1) \\&=50\end{aligned}$

Final Answer:-

The value of $1/2+(1/2+1/100)+(1/2+2/100)+.....+(1/2+99/100)$ is 50.

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