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Q. 4

Expert-verified

Calculus

Found in: Page 624

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Which p-series converge and which diverge?

The p-test states that:

(i) For $p > 1$ , the series $\sum_{k = 1}^{\infty} \frac{1}{k^{p}}$ converges.

(ii) For $p = 1$ , the harmonic series $\sum_{k = 1}^{\infty} \frac{1}{k}$ diverges.

(iii) For $p < 0$ , the series $\sum_{k = 1}^{\infty} \frac{1}{k^{p}}$ diverges.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

p-series.

Step 2. To determine which p-series converge or diverge.

The p-test states that:

(i) For $p > 1$ , the series $\sum_{k = 1}^{\infty} \frac{1}{k^{p}}$ converges.

(ii) For $p = 1$ , the harmonic series $\sum_{k = 1}^{\infty} \frac{1}{k}$ diverges.

(iii) For $p < 1$ , the series $\sum_{k = 1}^{\infty} \frac{1}{k^{p}}$ diverges.

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