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,`...

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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.`

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