Evaluate: `("lim")_(nvecoo)(sumr=1nsqrt(r)sumr=1n1/(sqrt(r)))/(sumr=1n r)`

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)

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

The value of lim_(n rarr oo)(1*sum_(r=1)^(n)(r)+2*sum_(r=1)^(n-1)(r)+3sum_(r=1)^(n-2)(r)+....+n.1)/(n^(4))

m sum_(r=1)^(n)(1)/(n)sqrt((n+r)/(n-r))

The value of lim_(n rarr oo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^(2)) is equal to (1)/(35) (b) (1)/(4)(c)(1)/(10) (d) (1)/(5)

Evaluate :lim_(n rarr oo)sum_(r=1)^(n)(1)/((n^(2)+r^(2))^(1/2))

"lim_(n rarr oo)(1)/(n){sum_(r=1)^(n)e^((r)/(n))}=

Evaluate: lim_(n rarr oo) (sum_(r=0)^( n) (1)/(2^(r))) .