If `{x}` and `[x]` represent fractional and integral part of x respectively, find the value of `[x]+sum_(r=1)^(2000)({x+r})/2000`

Explanation

`[x]+sum_(r=1)^(2000)({x+r})/2000=[x]+sum_(r=1)^(2000)({x})/2000` [from property (i)]
`=[x]+({x})/2000sum_(r=1)^(2000)1=[x]+({x})/2000xx2000=[x]+{x}=x`