=(n-√20 10+√20 10-√2009)/(n-√20 10)
= 1+(√20 10-√2009)/(n-√20 10)
Let f (x) =1+(√ 2010-√ 2009)/(x-√ 2010).
Its image is exactly the same as y=(√20 10-√2009)/x, but the asymptote is different.
The image of f(x) here is a hyperbola with x=√20 10 and y= 1 as asymptotes.
Drawing display
Two positive integer n values closest to √20 10, the smallest term on the left and the largest term on the right!
44 & lt√20 10 & lt; 45
So a44 is the smallest term and a45 is the largest term.