🤷🏻‍♀️🤷🏻‍♀️ Does the p-series converge or diverge?!

Описание: We unravel the p-series test from AP Calculus, which can determine the convergence or divergence of series. This test applies to series in the specific form 1/n^p, where p is a constant.

The rule of thumb for the p-series test is simple: if p less than 1, the series converges; if p less than or equal to 1, the series diverges. An interesting case to note is when p is exactly 1, resulting in the series 1/n, known as the harmonic series. This particular series diverges, aligning with the principle that any series with p≤1 diverges.

#APCalculus #PSeriesTest #ConvergenceDivergence #MathEducation #CalculusExplained

Unit 10 of AP Calculus is all about Infinite Sequences and Series:
10.1 Defining Convergent and Divergent Infinite Series
10.2 Working with Geometric Series
10.3 The nth Term Test for Divergence
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as Power Series

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