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

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

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

Which of the following is the value of lim_(n rarr oo)sum_(r=1)^(n)(r^(3))/(r^(4)+n^(4))?

The value of lim_(n to oo)(1)/(n).sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2))) is equal to

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

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