If `f(n)=(1^2n+2^2 (n-1)+3^2 (n-2)+..+n^21)/(1^3+2^3+3^3+.....+n^3)` ,then (where [.] denotes greatest integer function)

If 1/1^3+[1+2]/[1^3+2^3]+[1+2+3]/[1^3+2^3+3^3]+..... upto n terms,then lim_(n->oo)[S_n], where [.] denotes the greatest integer function.

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

Let R=(2+sqrt3)^(2n) and f=R-[R] where [ ] denotes the greatest integer function , then R(1-f)=

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 solution set of the equation [n]^(2)+[n+1]-3=0 (where [. ] denotes greatest integer function is

show that [(sqrt(3) +1)^(2n)] + 1 is divisible by 2^(n+1) AA n in N , where [.] denote the greatest integer function .

show that [(sqrt(3) +1)^(2n)] + 1 is divisible by 2^(n+1) AA n in N , where [.] denote the greatest integer function .

" The solution set of the equation "[n]^(2)+[n+1]-3=0" (where [. ] denotes greatest integer function) is "

The value o lim_(xtooo)(1/(n^(3)))([1^(2)x+1^(2)]+[2^(2)x+2^(2)]+…..+[n^(2)x+n^(2)]) is where [.] denotes the greatest integer function.

The value o lim_(xtooo)(1/(n^(3)))([1^(2)x+1^(2)]+[2^(2)x+2^(2)]+…..+[n^(2)x+n^(2)]) is where [.] denotes the greatest integer function.