For the serioes `2+(sqrt(2)+1/(sqrt(2)))+((2sqrt(2)-1)+1/2)+((3sqrt(2)-2)+1/(2sqrt(2)))+......`

(sqrt(3)+1+sqrt(3)+1)/(2sqrt(2))

1+(sqrt(2)-1)/(2sqrt((2)))+(3-2sqrt(2))/12+(5sqrt(2))/24sqrt(2)...

(1+sqrt(2))/(3-2sqrt(2))=A sqrt(2)+B

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

(1)/(sqrt(2)+sqrt(3))-(sqrt(3)+1)/(2+sqrt(3))+(sqrt(2)+1)/(2+2sqrt(2))

Find the angles of the triangle whose sides are (sqrt(3)+1)/(2sqrt(2)), (sqrt(3)-1)/(2sqrt(2)) and sqrt(3)/2 .

((2+sqrt(3))/2)/(1+(sqrt(3)+1)/2) + ((2-sqrt(3))/2)/(1-((sqrt(3)-1)/2))

(sqrt3 + 1)/(2sqrt2) + (sqrt3 - 1)/(2sqrt2)

The matrix A={:[((1)/(sqrt(2)),(1)/(sqrt(2))),((-1)/(sqrt(2)),(-1)/(sqrt(2)))]:} is

The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals