Prove that `f(x)= Lt_(n->oo) sum_(r=1)^n ([rx])/n^2` is continuous for all x. Here [x] denotes greatest integer `<= x.`

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

Lt_(x to oo) ([x])/(x) (where[.] denotes greatest integer function )=

lim_(x->0) (lnx^n-[x])/[x], n in N where [x] denotes the greatest integer is

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

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

lim_ (x rarr oo x rarr oo in r) ([2x]) / (x) (where [x] denotes greatest integer <= x)

Prove that lim_(x->a^+) [x]=[a] for all a in R, where [*] denotes the greatest integer

If n = any integer , show that the function f(x)=[x]+[-x] has removable discontinuity at x=n , here [x] denotes greatest integer function.

int_(-n)^(n)(-1)^([x])backslash dx when n in N= in all of these [.] denotes the greatest integer function

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