If n E N and `a_n = 2^2 + 4^2 + 6^2 + ....+ (2n)^2` and `b=1^2 + 3^2 + 5^2 + ...(2n - 1)^2`. Find the value `Lim_(n->oo) ((sqrt(a_n)-sqrt(b_n))/(sqrtn))`

If nEN and a_(n)=2^(2)+4^(2)+6^(2)+....+(2n)^(2) and b=1^(2)+3^(2)+5^(2)+...(2n-1)^(2). Find the value lim_(n rarr oo)((sqrt(a_(n))-sqrt(b_(n)))/(sqrt(n)))

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

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

The value of lim_(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1)) is

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

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

lim_(nto oo)[(sqrt(n+1)+sqrt(n+2)+...+sqrt(2)n)/(sqrt(n^(3)))]

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

Evaluate the limit. lim_(n to oo) (sqrt(n+1)+sqrt(n+2)+……..+ sqrt(n+n))/(nsqrt(n))