Consider the power series

$\displaystyle \sum \frac{a^{n+1}}{n+1}\, {(-3)}^{n+1}$

The problem is: there is only one value of a for which the series is conditionally convergent. Find it.

For a = 1/3, the series is alternating and convergent. For a = -1/3, it diverges. I can't think of any number for which it becomes conditionally convergent.

Any help would be appreciated.