lim_(n rarr oo)root(1)(sqrt(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+cdots+(1)/(n)]

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

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(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+(1)/(sqrt(6n-3^(2)))+....+1/n)=

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

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]

lim_(n rarr oo)(sqrt(n+1)-sqrt(n))=0

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

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

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)))]