y=(e^(n)+1)/(e^(n))*n10sqrt(2)x^(2)+sqrt(a)n^(n)2

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

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)/(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

If n is a positive integer, which of the following two will always be integers: (I) (sqrt(2)+1)^(2n)+(sqrt(2)-1)^(2n) (II) (sqrt(2)+1)^(2n)-(sqrt(2)-1)^(2n) (III) (sqrt(2)+1)^(2n+1)+(sqrt(2)-1)^(2n+1) (IV) (sqrt(2)+1)^(2n+1)-(sqrt(2)-1)^(2n+1)

If a_(n) and b_(n) are positive integers and a_(n)+sqrt(2b_(n))=(2+sqrt(2))^(n), then lim_(x rarr oo)((a_(n))/(b_(n)))= a.2 b.sqrt(2)c.e^(sqrt(2))d.e^(2)

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)))

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_(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-

Lt_(n rarr oo)[(1)/(n)+(1)/(sqrt(n^(2) -1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+... "to n terms"]