Prove the following statements using strong induction: n 1. Σ γ = i=0 1-p+1 1-r for every non-negative integer n and every real number r 1. 2. Suppose that a store offers gift certificates in denominations of $3 and $5. Then any item priced at an integer number of dollars of value at least $8 can be paid for with these gift certificates without a need to use any other form of currency. For example, an item priced $16 can be paid with two $3 gift certificates and two $5 gift certificates.
Prove the following statements using strong induction: n 1. Σ γ = i=0 1-p+1 1-r for every non-negative integer n and every real number r 1. 2. Suppose that a store offers gift certificates in denominations of $3 and $5. Then any item priced at an integer number of dollars of value at least $8 can be paid for with these gift certificates without a need to use any other form of currency. For example, an item priced $16 can be paid with two $3 gift certificates and two $5 gift certificates.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Prove the following statements using strong induction:
n
1. Σ
i=0
1-p²+1
1-r
for
every non-negative integer n and every real number r ‡ 1.
2. Suppose that a store offers gift certificates in denominations of $3 and $5. Then any item
priced at an integer number of dollars of value at least $8 can be paid for with these gift certificates
without a need to use any other form of currency. For example, an item priced $16 can be paid with
two $3 gift certificates and two $5 gift certificates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd08e19be-7e5e-4944-9492-2c1f0e254c97%2F52e3acbc-0e67-4154-ad56-258f44b65c7a%2Fplyxnm_processed.png&w=3840&q=75)
Transcribed Image Text:Prove the following statements using strong induction:
n
1. Σ
i=0
1-p²+1
1-r
for
every non-negative integer n and every real number r ‡ 1.
2. Suppose that a store offers gift certificates in denominations of $3 and $5. Then any item
priced at an integer number of dollars of value at least $8 can be paid for with these gift certificates
without a need to use any other form of currency. For example, an item priced $16 can be paid with
two $3 gift certificates and two $5 gift certificates.
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