Essential Concepts
- The comparison tests are used to determine convergence or divergence of series with positive terms.
- When using the comparison tests, a series ∞∑n=1an is often compared to a geometric or p-series.
Glossary
- comparison test
- if 0≤an≤bn for all n≥N and ∞∑n=1bn converges, then ∞∑n=1an converges; if an≥bn≥0 for all n≥N and ∞∑n=1bn diverges, then ∞∑n=1an diverges
- limit comparison test
- suppose an,bn≥0 for all n≥1. If limn→∞anbn→L≠0, then ∞∑n=1an and ∞∑n=1bn both converge or both diverge; if limn→∞anbn→0 and ∞∑n=1bn converges, then ∞∑n=1an converges. If limn→∞anbn→∞, and ∞∑n=1bn diverges, then ∞∑n=1an diverges
Candela Citations
CC licensed content, Shared previously
- Calculus Volume 2. Authored by: Gilbert Strang, Edwin (Jed) Herman. Provided by: OpenStax. Located at: https://openstax.org/books/calculus-volume-2/pages/1-introduction. License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike. License Terms: Access for free at https://openstax.org/books/calculus-volume-2/pages/1-introduction