If `lim_(n->oo)(sum_(r=1)^nsqrt(r)sum_(r=1)^n1/(sqrt(r)))/(sum_(r=1)^nr)=k/3` then the value of k is

If lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(r)))/(sum_(r=1)^(n)r)=(k)/(3) then the value of k is

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)

Evaluate: lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(tau)))/(sum_(r=1)^(n)r)

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(n) and sum_(r=0)^(n)(C_(r))/(r+1)=k then the value of k is

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

If sum_(r=1)^(n) r(sqrt(10))/(3)sum_(r=1)^(n)r^(2),sum_(r=1)^(n) r^(3) are in G.P., then the value of n, is

sum_(r=1)^(n) r^(2)-sum_(r=1)^(n) sum_(r=1)^(n) is equal to

lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))