`lim_(x->oo)sum_(r=1)^n (x+r)^2010/((x^1006+1)(2x^1004+1))=`

lim_(xrarroo) (sum_(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))=

Evaluate lim_(x to 1) sum_(k=1)^(100) x^(k) - 100)/(x-1).

Let f(x)=lim_(nrarroo) sum_(r=0)^(n-1)(x)/((rx+1){(r+1)x+1}) . Then

Evaluate the following limit: lim_(nto oo)(sum_(r=1)^(n) sqrt(r)sum_(r=1)^(h)1/(sqrt(r)))/(sum_(r=1)^(n)r)

("lim")_(n->oo)sum_(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (c) 19 (d) 20

lim_(x->-oo)(x^2*tan(1/x))/(sqrt(8x^2+7x+1)) is

The value of lim_(n->oo)sum_(r=0)^(n) (sum_(t=0)^(r-1)1/(5^n)*"^n C_r * "^r C_t .(3^t)) is equal to

Let f(x)=(lim)_(x rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

lim_(xto0^(+)) (sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where ninN and [.] denotes the greatest integer function, equals