Jul 23, 2025 · P-series test is a fundamental tool in mathematical analysis used to determine the convergence or divergence of a specific type of infinite series known as p-series.

A p-series is a special type of series where terms are added (summed) together in a certain format. Simple definition, examples.

Jun 30, 2023 · The P Series Test: Explore its definition, applications, and examples. Learn how this mathematical tool is used in various contexts.

Recall from The p-Series Test page that: Theorem (p-Series Test): The special series $\sum_ {n=1}^ {\infty} \frac {1} {n^p}$ is convergent if $p > 1$ and divergent if $p ≤ 1$. We will now look at some …

If p > 1, the series will converge, and if p 1, the series diverges.

APPROACH: -Series form. Notice when the base is changing and the power is a xe Pick o the power p. State clearly what the value p equals. Determine and then state if p is greater than 1 or : : : less or …

We introduce p-series, and the simple p-series test to determine if a p series converges or diverges. We'll apply the p-series test in several examples, which require us to...

ntroduce a new family of series called p-series. For these series you can tell at an instant whether they converge or diverge and you can use them for comparison in the comparison tests or you may also …

P-series are typically used as a test of convergence; if p > 1, the p-series converges; if 0 < p ≤ 1, the p-series diverges. This test is referred to as the p-series test, and is a corollary of the integral test.

Read what a p-series is and some examples of it. Learn the harmonic series and the p-series test for convergence to prove if it is convergent or divergent.