sum_(n=1)^oo (3/p)^n Find the positive values of p for which the series converges.

This series is the sum of an infinite geometrical progression with the common ratio of  3/p. It is well known that such a series converges if and only if its common ratio is less than 1 by the absolute value.
In this problem we have the condition  |3/p| lt 1, or  |p| gt 3. Because we are asked about positive p's, we have  p gt 3.
The answer: for positive p this series converges if and only if  p gt 3. 
http://tutorial.math.lamar.edu/Classes/CalcII/Series_Special.aspx