{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW4 - 5 Problem 3.26 Page 73 Give an induction proof where...

This preview shows page 1. Sign up to view the full content.

Math 23b Homework 4 Spring, 2009 Due Wednesday, March 4. Be sure to write clearly, using complete sentences. Do not use abbreviations like s.t., w/, w/o, b/c, c/o, etc. In all problems you must prove that your answer is correct, even if the problem does not explicitly ask you to do so. 1. Problem 3.2 Page 71. Hint: What is a statement that should be true for all n ? 2. Problem 3.17 Page 72. 3. Problem 3.22 Page 72. Note that a 1 , .., a n R . You should use the Triangle Inequality in your inductive step. 4. Problem 3.23 Page 72.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5. Problem 3.26 Page 73. Give an induction proof, where P ( n ) is the statement that a n = n 3-n + 1. 6. Problem 3.30 Page 73. Do this without using induction. Use two results we have proved in class. 7. Problem 3.57 Page 75. The word sequence means list. There is a typo: replace “ n ≥ 2” by “ n ≥ 3.” In the inductive step, assume 1 ≤ a n-2 ≤ 2 and 1 ≤ a n-1 ≤ 2, and prove that the formula for a n gives a number between 1 and 2....
View Full Document

{[ snackBarMessage ]}