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If `[x]` and `{x}` represetnt the integral and fractional parts of `x ,` respectively, then the value of `sum_(r=1)^(2000)({x+r})/(2000)` is `x` (b) `[x]` (c) `{x}` (d) `x+2001`

A

x

B

[x]

C

{x}

D

x+2001

Text Solution

Verified by Experts

The correct Answer is:
C
`sum_(r=1)^(2000)({x+r})/(2000)=sum_(r=1)^(2000)({x})/(2000)=2000({x})/(2000)={x}.`
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