Correct Answer!

We hope that you properly chose the series for comparison. An example of appropriate comparison here would be:

1 2n-1

³

1 3n-1-1

.

Note that the most obvious series to compare our series to, i.e.

¥ å n = 2  1 3n-1

does not work. Because of the inequality

1 3n-1 £ 1 3n-1-1 ,

convergence of

¥ å n = 2  1 3n-1

does not imply convergence of

¥ å n = 2  1 3n-1 - 1 .

Note that this problem could also be solved using

• the Ratio Test,
• the Integral Test and
• the Limit Comparison Test.