1 / 12

Discrete Structures – CNS2300

Discrete Structures – CNS2300. Text Discrete Mathematics and Its Applications (5 th Edition) Kenneth H. Rosen Chapter 4 Counting. Section 4.4. Binomial Coefficients. Pascal’s Triangle. The Binomial Theorem. Let x and y be variables, and let n be a positive integer: Then.

dakota-hines
Download Presentation

Discrete Structures – CNS2300

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. Discrete Structures – CNS2300 Text Discrete Mathematics and Its Applications (5th Edition) Kenneth H. Rosen Chapter 4 Counting

  2. Section 4.4 Binomial Coefficients

  3. Pascal’s Triangle The Binomial Theorem Let x and y be variables, and let n be a positive integer: Then

  4. Let n be a positive integer. Then

  5. Pascal’s Identity

  6. Pascal’s Identity You are probably most familiar with this identity from Pascal’s Triangle, used in algebra. 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 1

  7. Pascal’s Identity You are probably most familiar with this identity from Pascal’s Triangle, used in algebra. 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 1 C(5,1)=C(4,0)+C(4,1)

  8. Pascal’s Triangle

  9. 1 1 2 3 5 8 13 21 Pascal’s Triangle 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 1

  10. Vandermonde’s Identity Let m, n, and r be nonnegative integers with r not exceeding either m or n. Then

  11. Let n be a positive integer. Then

  12. finished

More Related