For `x in R with |x| < 1,` the value of `sum_(n=0)^oo(1+n)x^n` is

If f:R rarr R is defined by f(x)=x-[x]-(1)/(2). for x in R, where [x]is the greatest integer exceeding x, then {x in R:f(x)=(1)/(2)}=

If f: R rarr R is defined by f(x)= x-[x]- 1/2 for x in R , where [x] is the greatest integer not exceeding x, then {x in R : f(x) + 1/2}=

If f : R rarr R and g: R rarr R are given by f(x)=|x| and g(x)={x} for each x in R , then |x in R : g(f(x)) le f(g(x))}=

If f : R -> R are defined by f(x) = x - [x] and g(x) = [x] for x in R , where [x] is the greatest integer not ex-ceeding x, then for every x in R, f(g(x))=

Let A={x in R : |x+1| = |x|+1} and B ={x in R : |x-1| = |x|-1} , Then

Let P = { x : x in R , |x| Q = {x:x in R , |x -1 |ge 2} P uu Q = R - S then set S is : (where R is the set of real number)

Let P = { x : x in R , |x| Q = {x:x in R , |x -1 |ge 2} P uu Q = R - S then set S is : (where R is the set of real number)