• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q. 4

Expert-verified Found in: Page 624 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # 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

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. ### Want to see more solutions like these? 