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  3. ZuAI AP College Board Calculus AB/BC
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Harmonic Series and p-Series

Next Topic - Comparison Tests for Convergence
Study Guide Overview

This study guide covers p-series in calculus, including their definition and the rules for convergence and divergence. It provides practice problems to determine convergence or divergence based on the value of p. The harmonic series is introduced as a special case of a p-series. Examples demonstrate simplification techniques for applying the p-series test.

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Previous Topic - Integral Test for ConvergenceNext Topic - Comparison Tests for Convergence

Question 1 of 7

Which of the following series is a p-series? 🤔

∑n=1∞12n\sum_{n=1}^{\infty} \frac{1}{2^n}∑n=1∞​2n1​

∑n=1∞nn2+1\sum_{n=1}^{\infty} \frac{n}{n^2+1}∑n=1∞​n2+1n​

∑n=1∞1n3\sum_{n=1}^{\infty} \frac{1}{n^{3}}∑n=1∞​n31​

∑n=1∞(−1)nn\sum_{n=1}^{\infty} \frac{(-1)^n}{n}∑n=1∞​n(−1)n​