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

lim_(n rarr oo)(1)/(n^(3))(sqrt(n^(2)+1)+2sqrt(n^(2)+2^(2))+...+n sqrt(n^(2)+n^(2))) is equal to

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

lim _(x to oo) (1)/(n ^(3))(sqrt(n ^(2)+1)+2 sqrt(n ^(2) +2 ^(2))+ .... + n sqrt((n ^(2) + n ^(2)))=:

lim_(n rarr oo)(1+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))))

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

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)/sqrt(n+1)=