Evaluate `lim_(n->oo)` `[sum_(r=1)^n1/2^r]` , where [.] denotes the greatest integer function.

lim_(xrarr oo) (logx)/([x]) , where [.] denotes the greatest integer function, is

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

f(x)=lim_(n rarr oo)sin^(2n)(pi x)+[x+(1)/(2)], where [.] denotes the greatest integer function,is

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

The value of lim(n rarr oo)((1.5)^(n)+[(1+0.0001)^(10000)]^(n)) where [.] denotes the greatest integer function is:

The value of sum_(r=1)^(1024)[log_(2)r] is equal to,(I.] 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 S=sum_(r=1)^(117)(1)/(2[sqrt(r)]+1) where [.) denotes the greatest integer function.The value of S is

The function f(x)=lim_(nrarroo)cos^(2n)(pix)+[x] is (where, [.] denotes the greatest integer function and n in N )