1 / 13

Discrete Structures

Discrete Structures. Chapter 5: Sequences, Mathematical Induction, and Recursion 5.1 Sequences. A mathematician, like a painter or poet, is a maker of patterns. – G. H. Hardy, 1877 – 1947 A Mathematician’s Apology, 1940. Definitions. Sequence

zoe
Télécharger la présentation

Discrete Structures

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 Chapter 5: Sequences, Mathematical Induction, and Recursion 5.1 Sequences A mathematician, like a painter or poet, is a maker of patterns. – G. H. Hardy, 1877 – 1947 A Mathematician’s Apology, 1940 5.1 Sequences

  2. Definitions • Sequence A sequence is a function whose domain is either all the integers between two given integers or all the integers greater than or equal to a given integer. We typically write a sequence as • Term Each individual element ak is called a term and is read “a sub k”. • Subscript The k in ak is called a subscript or index. • Initial Term The m may be any integer and is the subscript of the initial term. • Final Term The n must be greater than or equal to m and is the subscript of the final term. 5.1 Sequences

  3. Definitions • An infinite sequence is denoted by • An explicit formula or general formula for a sequence is a rule that shows how the values of ak depend on k. 5.1 Sequences

  4. Example – pg. 242 #1 • Write the first four terms of the sequences below. 5.1 Sequences

  5. Example – pg. 243 # 11 • Find explicit formulas for sequences of the form a1, a2, a3, … with the initial terms given. 5.1 Sequences

  6. Definitions 5.1 Sequences

  7. Definition 5.1 Sequences

  8. Theorem 5.1.1 5.1 Sequences

  9. Examples – pg. 243 • Compute the summations and products. 5.1 Sequences

  10. Example • Write using summation or product notation. 5.1 Sequences

  11. Definitions 5.1 Sequences

  12. Formula 5.1 Sequences

  13. Examples – pg. 243 • Compute each of the following. Assume the values of the variables are restricted so that the expressions are defined. 5.1 Sequences

More Related