Simplify

Algebra Level 4

$\large[X]+\displaystyle \sum_{i=1}^ {1000}\frac{\{X+i\}}{1000}$

Assumptions:

$\left [ A \right ]$ =the greatest integer function of $A$

$\{ A \}$ =the fractional part of $A$

1000+[X]

\{X\}

[X]

1000+{X}

X

1000

1 solution

Rachit Shukla
Apr 10, 2015

$[X]+\displaystyle \sum_{i=1}^ {1000}\frac{\{X+i\}}{1000}$

As $i$ is an integer,

$\Rightarrow$ $[X]+\frac{\{X\}}{1000}\displaystyle \sum_{i=1}^ {1000}i^0$

$\Rightarrow$ $[X]+\frac{\{X\}}{1000}1000$

$\Rightarrow$ $[X]+{\{X\}}$

$\Rightarrow$ Ans= $X$ $\ddot\smile$