Explanation

The correct answer is: ∑1/n^p converges if p > 1.

The p-series ∑1/n^p is a well-known series in mathematics, and its convergence properties are as follows:

• If p > 1, the series converges.
• If p ≤ 1, the series diverges.

This is because the terms of the series decrease slower than the terms of a geometric series with ratio less than 1 when p ≤ 1, and decrease faster than the terms of a geometric series with ratio less than 1 when p > 1.