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

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

lim_(n rarr oo)n[sqrt(n+1)-sqrt(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(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)sqrt(n+1))+(1)/(sqrt(n)sqrt(n+2))+......+(1)/(sqrt(n)sqrt(4n))

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