StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q. 4

Expert-verifiedFound in: Page 624

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.

*p-*series.

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.

94% of StudySmarter users get better grades.

Sign up for free