Property of greatest integer function (xi) `[x]+[x+1/n]+[x+2/n]+.........+[x+(n-1)/n]=[nx]; n inNN`

Prove that for every real number [x+[x+(1)/(n)]+[x+(2)/(n)]+...+[x+(n-1)/(n)]=[nx]

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function) then which of the following is correct a. n (b) 1 (c) 1/n (d) none of these

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function) then which of the following is correct a. n (b) 1 (c) 1/n (d) none of these

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function) then which of the following is correct a. n (b) 1 (c) 1/n (d) none of these

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function). (a) n (b) 1 (c) 1/n (d) none of these

Prove that [x]=[x/2]+[(x+1)/2] where [.] denote greatest integer function and n be any positive integer than show that [(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+…..=n

If [.] denotes the greatest integer function then find the value of lim_(n rarr oo)([x]+[2x]+...+[nx])/(n^(2))

Let f(x)=nx + n-[nx + n]+tan((pix)/ 2) , where 9, [x] is the greatest integers function le x and n in N.It is 1) a periodic function of period1 2) a periodic function of period 4 3) not periodic 4) a periodic function of period 2

Which of the following function is/are periodic? (a)f(x)={1,xi sr a t ion a l0,xi si r r a t ion a l (b)f(x)={x-[x]; 2n

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number