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

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+.......+(1)/(sqrt(n^(2)+(n-1)n))]=.........

lim_(n rarr oo)(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2) +2))+...(.1)/(sqrt(n^(2)+2n))=

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

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

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

lim_(n rarr oo)(1+sqrt(n))/(1-sqrt(n))

lim_(n rarr oo)[(1)/(sqrt(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+(1)/(sqrt(6n-) 3^(2)))+...+(1)/(n)]

Find lim_(n rarr oo)S_(n); if S_(n)=(1)/(2n)+(1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-4))+......+(1)/(sqrt(3n^(2)+2n-1))