=(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.