It's very important to have a feeling for how sequences compare with
each other.
Let's write:
 {a_{n}} >> {b_{n}}
 if (a_{n}/b_{n}) > + as n >

and
 {a_{n}} << {b_{n}}
 if
(a_{n}/b_{n}) > 0 as n >

(Think of >> as "infinitely bigger in the limit"
and << as "infinitely smaller in the limit")
Problem: Line up the following sequences,
deciding which is "first", "second", "third", etc so that:
first << second << third << fourth << fifth << sixth
a) (n)
 b) e^{n}
 c) n!
 d) n^{2}
 e) ln n
 f) n^{n}

HTML translation by Harel Barzilai of Activity by
Marshall Cohen.