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Calculus Sequences and Series Review List p-series, geometric series, ratio, root, integral comparison, alternating,
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30 lip 2024 · 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 defined by the general form: \sum_ {n=1}^ {\infty} \frac {1} {n^p} ∑n=1∞ np1. Where p is a positive real number.
30 cze 2023 · In the realm of mathematical analysis, determining whether a series converges or diverges is a fundamental question. The p-series test provides a valuable tool for investigating the behavior of a specific type of series known as the p-series.
The integral test, applied to the function f(x)=x−p=1/xp, is called the p-series test: the p-series 1−p+2−p+3−p+… is convergent if 1">p>1 and divergent otherwise, if p≤1. (In fact, when 1">p>1, the Riemann zeta function ζ is defined by this series: ζ(p):=1−p+2−p+3−p+….)
4 mar 2014 · The series themselves aren't used explicitly most of the time, but the computation methods are derived from them. Often the simplest way to express a result is as a series, to get the numerical value you need to compute it's value.
