Explanation Proof: The relation is d n + 1 = 0.5 d n + 100 , d 1 = 100 , for n = 1 , 2 , 3 , ⋯ (1) To prove that d n bounded by 200 for all n by induction. Base case: n = 1 To prove that the claim is true when n = 1 . d 1 = 100 < 200 Therefore, the claim is true when n = 1 . Induction hypothesis: n = k Assume that the claim is true when n = k . d k ≤ 200 Induction step: n = k + 1 To prove that the claim is true when n = k + 1 . Substitute k + 1 for n in equation (1), d k + 1 = 0

2nd Edition

ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 8.2, Problem 96E

To determine

To prove: The drug dose sequence in Example 5, dn+1=0.5dn+100,d1=100, for n=1,2,3,⋯ is bounded and monotonic.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 95E

Chapter 8.2, Problem 97E

Students have asked these similar questions

L₁ = {anzman: n≥0,m≥ 0} Use the rule of contradiction, prove that following language is regular or not.

Second order Spada numbers are well established in the insurance industry. Formally they are defined by the recurrence: Si={Si−1 %( Si−2+1) :i≥ 2 , 1:i=0 ,7 :i=1} Give an O(n) time algorithm to compute the n-th Second order Spada number

= For integer n ≥ 1 let P(n) be the predicate that 9" - 5n CEZ 4c for some For the induction hypothesis, consider k ≥ 1, and suppose that P(k) is true. For the inductive step, we want to show that P(k+1) is true. True or false: The following proof correctly proves P(k+ 1) true, where every step other than the one labelled IH follows by algebra. (I'm asking: is this a valid algebraic proof? Is the algebra correct? Did I use the IH correctly? Did I get the correct final result?) 9k+15k+19.9k - 5.5k True False = 9(4c – 5k) – 5 ⋅ 5% for CE Z by the IH = 4.9c-9.5k - 5.5k = 4.9c-4.5k = 4d for d = Z

Chapter 8 Solutions

CODE/CALC ET 3-HOLE

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

To prove: The drug dose sequence in Example 5, d n + 1 = 0.5 d n + 100 , d 1 = 100 , for n = 1 , 2 , 3 , ⋯ is bounded and monotonic.

Solution Summary: The author concludes that the drug dose sequence in Example 5 is bounded and monotonic.

Concept explainers

Videos

To prove: The drug dose sequence in Example 5, dn+1=0.5dn+100,d1=100, for n=1,2,3,⋯ is bounded and monotonic.

Want to see the full answer?

Chapter 8 Solutions