Prove that for `n=1, 2, 3...` `[(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...=n` where `[x]` represents Greatest Integer Function

The value of int_0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N , is equal to where [.] represents greatest integer function. pi/2(2n-1)-2x pi/2(2n-1)+x pi/2(2n+1)-x (d) pi/2(2n+1)+x

Find the value of sum_(n=8)^100[{(-1)^n*n)/2] where [x] greatest integer function

If n is a natural number and 1 <= n <= 100 ,then the number of solutions of [(n)/(2)]+[(n)/(3)]+[(n)/(5)]=(n)/(2)+(n)/(3)+(n)/(5) (where [.] denotes the greatest integer function) is

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

Prove that 1+2+3+4......+N<(1)/(8)(2n+1)^(2)

Lim_(n->oo)(sqrt(n^2+n+1)-[n^2+n+1])(n in I) where [ ] denote the greatest integer functionis is

Let n be odd positive integer.(3+sqrt(5))^(n)-3[((3+sqrt(5))^(n))/(3)]=? ,where [..] represents greatest integer function.

Evaluate lim{n-> oo) ([1.2x]+[2.3x]+.....+[n.(n+1)x])/(n^3)), where [.] denotes greatest integer function.

Prove that 1*2+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)