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

If f(x) is continuous in [0,1] and f((1)/(2))=1 prove that lim_(n rarr oo)f((sqrt(n))/(2sqrt(n+1)))=1

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

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

Let u_(n)=sum_(k=1)^(n)(k) and v_(n)=sum_(k=1)^(n)(k-0.5) . Then lim_(n rarr oo)(sqrt(u_(n))-sqrt(v_(n))) equals

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)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))

lim_(n rarr oo)(sqrt(n^(2)+n)-sqrt(n^2+1))

The value of lim_(n rarr oo)(sqrt(3n^(2)-1)-sqrt(2n^(2)-1))/(4n+3) is

The value of lim_(n rarr oo)(1/sqrt(4n^(2)-1)+1/sqrt(4n^(2)-4)+...+1/sqrt(4n^(2)-n^(2))) is -

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