If `[x]` and `{x}` represetnt the integral and fractional parts of `x ,` respectively, then the value of `sum_(r=1)^(1000)({x+r})/(1000)` is

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 (a)x (b) [x]( c) {x} (d) x+2001

If [x] and {x| denotes the greatest integer function and fractional part respectively,then the value of sum_(r=1)^(2000)({x+r})/(2000)

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

If [x] and {x} represent integral and fractional part of x then the function defined by f(x)=[x]+sum_(r=1)^(1000)({x+r})/(1000) is equal to (A) 2[x]+{x} (B) 4x (C) x (D) 4[x]+1000{x}

If [x] and {x} represent integral and fractional part of x then the function defined by f(x)=[x]+sum_(r=1)^(1000)({x+r})/(1000) is equal to (A) 2[x]+{x} (B) 4x (C) x (D) 4[x]+1000{x}

Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral int_(0)^(5)[x]{x}dx is -

If [x]-{x}=(x)/(3), where [1,{} represents greatest integer function and fractional part function respectively,then value of (10 lambda)/(3) where lambda is sum of values of x satisfying it,is

If {x} and [x] represent fractiona and integral part of x respectively then solve the equation x-1=(x-[x])(x-{x})