`lim_(n rarr oo)(1)/(n^(4))sum_(r=1)^(n)r^(3)=`

The value of lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)((r)/(n+r)) is equal to

If f(x) is integrable over [1,], then int_(2)^(2)f(x)dx is equal to lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)f((r)/(n))lim_(n rarr oo)(1)/(n)sum_(r=n+1)^(2n)f((r)/(n))lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)f((r+n)/(n))lim_(n rarr oo)(1)/(n)sum_(r=1)^(2n)f((r)/(n))

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

lim_(n rarr oo)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2))) equals

lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=

lim_ (n rarr oo) (1) / (n ^ (4)) sum_ (r = 1) ^ (n) r (r + 2) (r + 4) =

alpha=lim_(n rarr oo)sum_(i=1)^(n)sum_(j=1)^(i)(j)/(n^(3)), then [(1)/(alpha)-1] is

lim_(n rarr oo)(sum_(r=1)^(n)r^(1/a)(n^(a-(1)/(a))+r^(a-(1)/(a))))/(n^(a+1))=

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