sqrt(2)n^(2)+7n+5sqrt(2)=0

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 4 cos 36^(@) + cot(7(1^(@))/(2)) = sqrt(n_(1)) + sqrt(n_(2)) + sqrt(n_(3)) + sqrt(n_(4)) + sqrt(n_(5)) + sqrt(n_(6)) then the product of the digits in sum_(i = 1)^(6) n_(i)^(2) =

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

If (sqrt(2n^(2)+n)-lambda sqrt(2n^(2)-n))=(1)/(sqrt(2))( where lambda is real number),then

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

Find underset( n rarr oo) ("lim") (sqrt( n^(2) + 1)+ sqrt( n ) )/( sqrt( n ^(2) + 1)- sqrt( n ) )

1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+ n terms is equal to a. ((sqrt(3n +2))-sqrt(2))/(3) b.(n)/(sqrt(2+3n)+sqrt(2)) c.less than n d.less than sqrt(n/3)

The value of lim_(nto oo)(1/(sqrt(n^(2)))+1/(sqrt(n^(2)+1))+…..+1/(sqrt(n^(2)+2n))) is

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) +-1n((sqrt(3)+sqrt(7))/2)