Solution of Problem 5 - Limit Comparison Test
Using the , we compare our original series åan
to the series
| Since
|
|
|
lim
n® ¥
|
|
an
bn
|
= |
lim
n® ¥
|
|
3n-1
3n-1-1
|
= 1 is finite and positive, |
|
|
and since the series åbn is a convergent () series, we
conclude that our series converges.
Furthermore, since our series has only positive terms, its convergence is
.
Note that this problem could also be solved using