The value of `lim_(x->0)[(1-2x)^nsum_(r=0)^n_r((x+x^2)/(1-2x))^r]^(1/ x)` is :

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is a. 0 b. -log2 c. 1 d. e

Evaluate lim_(n->oo)1/nsum_(r=n+1)^(2n)log_e(1+r/n)

The value of lim_(xrarr1)Sigma_(r=1)^(10)=(x^(r )-1^(r ))/(2(x-1)) is equal to

The value of lim_(xrarr1)Sigma_(r=1)^(10)=(x^(r )-1^(r ))/(2(x-1)) is equal to

lim_(n->oo)1/nsum_(r=1)^(2n)r/(sqrt(n^2+r^2)) equals

If alpha and beta are the roots of the equation 375x^(2)-25x-2=0, then the value of lim_(n rarr oo)(sum_(r=1)^(n)alpha^(r)+sum_(r=1)^(n)beta^(r)) is

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

lim_(x rarr2)(sum_(r=1)^(n)x^(r)-sum_(r=1)^(n)2^(r))/(x-2)

lim_(xrarr2)(sum_(r=1)^(n)x^r-sum_(r=1)^(n)2r)/(x-2) is equal to

lim_(n rarr oo) n.sum_(r=0)^(n-1) 1/(n^(2)+r^(2)) =