underset n rarr oo Lt(1)/(n^(2))sum_(r=1)^(n)r*e^(r/n)

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

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

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

{:(" " Lt),(n rarroo):}(1)/(n^(2)) sum_(r=1)^(n) r.e^(r//n)=

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

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^(3)) sum_(r = 1)^(n) r^(2) is :

lim_(x rarr oo) (1)/(n^(4)) sum_(r = 1)^(n) r^(3) is :