[sirio11]

Usually simple algebra and mathematical induction will do it.

Using Jason's example

You want to compare

a(n) and a(n+1)

[n/(n^2+1)] and [(n+1)/((n+1)^2+1)]

cross multiply

n[((n+1)^2+1] and (n+1)(n^2+1)

n^3+2n^2+n+1 and n^3+n^2+n+1

n^2 and 0 which is obviously >

Go back and then a(n) > a(n+1) therefore decreasing