CSE215_MR_slides_Fall2018_10.pdf - CSE215 Lecture 10 Oct 1st,2018 CS Stonybrook Univ Martin Radfar 1 Quiz 2 Solution \u2022 Prove that For all integers a b

CSE215_MR_slides_Fall2018_10.pdf - CSE215 Lecture 10 Oct...

This preview shows page 1 - 18 out of 18 pages.

CSE215 Lecture 10 Oct 1st,2018 CS, Stonybrook Univ. Martin Radfar 1
Image of page 1
Quiz 2 Solution Prove that For all integers a , b , and c if a | b ,and a c, then a (b+c) 2
Image of page 2
Solution 1 3
Image of page 3
Solution 2 4
Image of page 4
Sample Exam Problems 1-Prove or disprove sum of two positive irrational numbers is irrational 2- prove that there exists a unique prime number of the form n 2 +2 n -3 where n is positive integer. 3- Prove that for all integers a if a 3 is even then a is even. 5
Image of page 5
6
Image of page 6
Arithmetic Sequences 7
Image of page 7
Geometric Sequences 8
Image of page 8
Repeating decimals 9
Image of page 9
Finding Terms of Sequences Given by Explicit Formulas Define sequences a 1 , a 2 , a 3 ,… and b 2 , b 3 , b 4 ,… by the following explicit formulas: Compute the first five terms of both sequences. Solution:
Image of page 10
Solution cont’d
Image of page 11
Product Notation
Image of page 12
Product Notation A recursive definition for the product notation is the following: If m is any integer, then
Image of page 13
Example Compute the following products: a. b. Solution: a. b.
Image of page 14
Properties of Summations and Products
Image of page 15
Example
Image of page 16
Image of page 17
Image of page 18

You've reached the end of your free preview.

Want to read all 18 pages?

  • Spring '20
  • Numerical digit, Positional notation, Decimal, Rational number, Numeral system

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture