Question

If [x] and {x} represent integral and fractional parts of x, then the expression $\left[x\right]+\sum _{r=1}^{2000}\frac{\left\{x+r\right\}}{2000}$ is equal to

• A. $\frac{2001}{2}x$
• B. $x+200$
• C. $x$
• D. $\left[x\right]+\frac{2001}{2}$

Answer 1

The correct option is C $x$

$\left[x\right]+\sum _{r=1}^{2000}\frac{\{x+r\}}{2000}$

$\left[x\right]+\frac{\{x+1\}}{2000}+\frac{\{x+2\}}{2000}+........+\frac{\{x+2000\}}{2000}$
$\left[x\right]+\frac{2000\left\{x\right\}}{2000}=x$