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

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

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

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

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

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

The value of lim_(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] denotes the greatest integer function is

The value of lim_(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) 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