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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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In each of 21 and 22, a sequence is specified by a recurr ence relation and initial conditions. In each case, (a) use iteration to guess an explicit formula for the sequence; (b) use strong mathematical induction to confirm the corr ectness of the formula you obtained in part (a).

22. b k = b k / 2 + 1 , for each integer k 2 b 1 = 1 .

To determine

(a)

Use iteration to guess an explicit formula for the given sequence.

Explanation

Given information:

A sequence is specified by a recurrence relation and initial conditions.

bk=bk/2+2, for all integers k2, b1=1

Calculation:

Given:

bk=bk/2+2, for all integers k2, b1=1

Let us determine the first terms of the given recurrence relation:

b1=1=1+2log21

b2=b2/2+2=b1+2=1+2=3=1+2log22

b3=b3/2+2=b2+2=3+2=5=1+2log23

b4=b4/2+2=b2+2=3+2=5=1+2log24

b5=b5/2+2=b3+2=5+2=7=1+2log25

b6=b

To determine

(b)

Use strong mathematical induction to confirm the correctness of the formula we obtain in part (a).

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Chapter 11 Solutions

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Sect-11.1 P-5ESSect-11.1 P-6ESSect-11.1 P-7ESSect-11.1 P-8ESSect-11.1 P-9ESSect-11.1 P-10ESSect-11.1 P-11ESSect-11.1 P-12ESSect-11.1 P-13ESSect-11.1 P-14ESSect-11.1 P-15ESSect-11.1 P-16ESSect-11.1 P-17ESSect-11.1 P-18ESSect-11.1 P-19ESSect-11.1 P-20ESSect-11.1 P-21ESSect-11.1 P-22ESSect-11.1 P-23ESSect-11.1 P-24ESSect-11.1 P-25ESSect-11.1 P-26ESSect-11.1 P-27ESSect-11.1 P-28ESSect-11.2 P-1TYSect-11.2 P-2TYSect-11.2 P-3TYSect-11.2 P-4TYSect-11.2 P-5TYSect-11.2 P-6TYSect-11.2 P-1ESSect-11.2 P-2ESSect-11.2 P-3ESSect-11.2 P-4ESSect-11.2 P-5ESSect-11.2 P-6ESSect-11.2 P-7ESSect-11.2 P-8ESSect-11.2 P-9ESSect-11.2 P-10ESSect-11.2 P-11ESSect-11.2 P-12ESSect-11.2 P-13ESSect-11.2 P-14ESSect-11.2 P-15ESSect-11.2 P-16ESSect-11.2 P-17ESSect-11.2 P-18ESSect-11.2 P-19ESSect-11.2 P-20ESSect-11.2 P-21ESSect-11.2 P-22ESSect-11.2 P-23ESSect-11.2 P-24ESSect-11.2 P-25ESSect-11.2 P-26ESSect-11.2 P-27ESSect-11.2 P-28ESSect-11.2 P-29ESSect-11.2 P-30ESSect-11.2 P-31ESSect-11.2 P-32ESSect-11.2 P-33ESSect-11.2 P-34ESSect-11.2 P-35ESSect-11.2 P-36ESSect-11.2 P-37ESSect-11.2 P-38ESSect-11.2 P-39ESSect-11.2 P-40ESSect-11.2 P-41ESSect-11.2 P-42ESSect-11.2 P-43ESSect-11.2 P-44ESSect-11.2 P-45ESSect-11.2 P-46ESSect-11.2 P-47ESSect-11.2 P-48ESSect-11.2 P-49ESSect-11.2 P-50ESSect-11.2 P-51ESSect-11.3 P-1TYSect-11.3 P-2TYSect-11.3 P-3TYSect-11.3 P-1ESSect-11.3 P-2ESSect-11.3 P-3ESSect-11.3 P-4ESSect-11.3 P-5ESSect-11.3 P-6ESSect-11.3 P-7ESSect-11.3 P-8ESSect-11.3 P-9ESSect-11.3 P-10ESSect-11.3 P-11ESSect-11.3 P-12ESSect-11.3 P-13ESSect-11.3 P-14ESSect-11.3 P-15ESSect-11.3 P-16ESSect-11.3 P-17ESSect-11.3 P-18ESSect-11.3 P-19ESSect-11.3 P-20ESSect-11.3 P-21ESSect-11.3 P-22ESSect-11.3 P-23ESSect-11.3 P-24ESSect-11.3 P-25ESSect-11.3 P-26ESSect-11.3 P-27ESSect-11.3 P-28ESSect-11.3 P-29ESSect-11.3 P-30ESSect-11.3 P-31ESSect-11.3 P-32ESSect-11.3 P-33ESSect-11.3 P-34ESSect-11.3 P-35ESSect-11.3 P-36ESSect-11.3 P-37ESSect-11.3 P-38ESSect-11.3 P-39ESSect-11.3 P-40ESSect-11.3 P-41ESSect-11.3 P-42ESSect-11.3 P-43ESSect-11.4 P-1TYSect-11.4 P-2TYSect-11.4 P-3TYSect-11.4 P-4TYSect-11.4 P-5TYSect-11.4 P-1ESSect-11.4 P-2ESSect-11.4 P-3ESSect-11.4 P-4ESSect-11.4 P-5ESSect-11.4 P-6ESSect-11.4 P-7ESSect-11.4 P-8ESSect-11.4 P-9ESSect-11.4 P-10ESSect-11.4 P-11ESSect-11.4 P-12ESSect-11.4 P-13ESSect-11.4 P-14ESSect-11.4 P-15ESSect-11.4 P-16ESSect-11.4 P-17ESSect-11.4 P-18ESSect-11.4 P-19ESSect-11.4 P-20ESSect-11.4 P-21ESSect-11.4 P-22ESSect-11.4 P-23ESSect-11.4 P-24ESSect-11.4 P-25ESSect-11.4 P-26ESSect-11.4 P-27ESSect-11.4 P-28ESSect-11.4 P-29ESSect-11.4 P-30ESSect-11.4 P-31ESSect-11.4 P-32ESSect-11.4 P-33ESSect-11.4 P-34ESSect-11.4 P-35ESSect-11.4 P-36ESSect-11.4 P-37ESSect-11.4 P-38ESSect-11.4 P-39ESSect-11.4 P-40ESSect-11.4 P-41ESSect-11.4 P-42ESSect-11.4 P-43ESSect-11.4 P-44ESSect-11.4 P-45ESSect-11.4 P-46ESSect-11.4 P-47ESSect-11.4 P-48ESSect-11.4 P-49ESSect-11.4 P-50ESSect-11.4 P-51ESSect-11.5 P-1TYSect-11.5 P-2TYSect-11.5 P-3TYSect-11.5 P-4TYSect-11.5 P-5TYSect-11.5 P-1ESSect-11.5 P-2ESSect-11.5 P-3ESSect-11.5 P-4ESSect-11.5 P-5ESSect-11.5 P-6ESSect-11.5 P-7ESSect-11.5 P-8ESSect-11.5 P-9ESSect-11.5 P-10ESSect-11.5 P-11ESSect-11.5 P-12ESSect-11.5 P-13ESSect-11.5 P-14ESSect-11.5 P-15ESSect-11.5 P-16ESSect-11.5 P-17ESSect-11.5 P-18ESSect-11.5 P-19ESSect-11.5 P-20ESSect-11.5 P-21ESSect-11.5 P-22ESSect-11.5 P-23ESSect-11.5 P-24ESSect-11.5 P-25ESSect-11.5 P-26ES