Solution of Problem 5 - Ratio Test

We use the :

lim
n® ¥

| a_n+1|

| a_n|

=

lim
n® ¥

3^n-1-1

3ⁿ-1

=

lim
n®¥

1/3-3^-n

1-3^-n

=

1

3

< 1

Thus, the series .

Note that this problem could also be solved by

the Limit Comparison Test and
the Integral Test.