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

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

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

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

lim_(n rarr4)(sqrt(2n+1)-3)/(sqrt(n-1)-sqrt(2))

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

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^(2)+n)-sqrt(n^2+1))

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

lim_ (n-> oo) (sqrt (n))/(sqrt (n)+sqrt (n+1)) = (i) 1 (ii) 1/2 (iii) 0 (iv) infty

The Sequence {a_(n)}_(n=1)^(+oo) is defined by a_(1)=0 and a_(n+1)=a_(n)+4n+3,n>=1 . Find the value of lim_(n rarr+oo)(sqrt(a_(n))+sqrt(a_(4n))+sqrt(a_(4^(2)n))+sqrt(a_(4^(3)n))+......+sqrt(a_(4^(10)n)))/(sqrt(a_(n))+sqrt(a_(2n))+sqrt(a_(2^(2)n))+sqrt(a_(2^(3)n))+.....+sqrt(a_(2^(10)n)))