`lim_(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+...+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]`

{:(" "Lt),(n rarr oo):} [(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+(sqrt(n^(2)-3^(2)))/(n^(2)).+....n "terms"]=

underset(nrarroo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+....+(1)/(sqrt(n^(2)-(n-1)^(2)))) is equal to

lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))} is equal to-

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

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

Lt_(n rarr oo)[(1)/(n)+(1)/(sqrt(n^(2) -1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+... "to n terms"]

Evaluate: lim_(n rarr oo)((1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-2^(2)))+...+(1)/(sqrt(3n^(2))))