Concept:

A p-series is a specific type of infinite series. It's a series of the form as shown below,

\(\mathop \sum \nolimits_{n = 1}^\infty \frac{1}{{{n^p}}} = \frac{1}{{{1^p}}}+\frac{1}{{{2^p}}}+\frac{1}{{{3^p}}}+... \)

where p can be any real number greater than zero.

Notice that in this definition n will always take on positive integer values, and the series is an infinite series because it's a sum containing infinite terms.

There are infinitely many p-series because you have infinite choices for p. Each time you choose a different value for p you create another p-series.

With p-series,

If p > 1, the series will converge, or in other words, the series will add up to a specific numerical value.

If 0 < p ≤ 1, the series will diverge, which means that the series won't add up to a specific numerical value.