It's very important to have a feeling for how sequences compare with
each other.
Let's write:
| {an} >> {bn}
| if (an/bn) -> + as n ->
|
and
| {an} << {bn}
| if
(an/bn) -> 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) en
| c) n!
| d) n2
| e) ln n
| f) nn
|
HTML translation by Harel Barzilai of Activity by
Marshall Cohen.