On-line Math 21

Example 1 b_n = 2ⁿ

[Solution]This sequence is just the denominators of the previous example. As n increases, b_n = 2ⁿ increases very quickly, and increases without bound. So, we say that this sequence diverges, or has no limit as n goes to infinity. It is a bit more precise to say that the sequence goes to infinity in the limit, or

lim n® ¥  2n = ¥,

since what happens is that the terms continue to grow (as opposed to varying randomly).

[Back] 

Copyright (c) 2000 by David L. Johnson.