1 / 4

The Direct Comparison Test (Note: all terms must be positive)

The Direct Comparison Test (Note: all terms must be positive). Part 1 The series diverges if there exists another series such that b n < a n and b n diverges, then the series diverges. Part 2 The series converges if there exists another

deon
Download Presentation

The Direct Comparison Test (Note: all terms must be positive)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Direct Comparison Test (Note: all terms must be positive) Part 1 The seriesdiverges if there exists another seriessuch that bn < an and bn diverges, then the series diverges. Part 2 The seriesconverges if there exists another seriessuch that an <bn and bn converges, then the series converges.

  2. Example: Does the series converge?

  3. If , then both and converge or both diverge. Limit Comparison Test If and for all (N a positive integer) Note: To find an appropriate seies to compare with, consider leading terms of numerator and denominator of given series.

  4. Example: Does the series converge?

More Related