A p-series is a type of infinite series that takes the form \sum_n=1^\infty \frac1n^p, where p is a positive constant. The behavior of a p-series depends on the value of p. If p > 1, the series converges, meaning it approaches a finite value. If p \leq 1, the series diverges, indicating that it grows without bound. The convergence or divergence of p-series is an important concept in calculus and is often used in the study of series convergence and integral tests. Understanding p-series helps in analyzing the behavior of more complex series and functions in mathematics.