Suppose that a bank machine can dispense money in either 3$ or 10$ bills. Show that any amount over 17$ could be dispensed with combinations of only the 3$ or the 10$ bills

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter9: Integer Programming
Section9.2: Formulating Integer Programming Problems
Problem 9P
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discrete math 

1. Use mathematical induction to solve the following:
1
(a) Find a formula for
1.2
12 25
1
by examining the values of this expression for
2.3
п(п + 1)
small valucs of n.
(b) Show that 7" – 1 is a multiple of 6 for all n e N
2. Suppose that a bank machine can dispense money in either 3$ or 10$ bills. Show that any
amount over 17$ could be dispensed with combinations of only the 3$ or the 10$ bills
Transcribed Image Text:1. Use mathematical induction to solve the following: 1 (a) Find a formula for 1.2 12 25 1 by examining the values of this expression for 2.3 п(п + 1) small valucs of n. (b) Show that 7" – 1 is a multiple of 6 for all n e N 2. Suppose that a bank machine can dispense money in either 3$ or 10$ bills. Show that any amount over 17$ could be dispensed with combinations of only the 3$ or the 10$ bills
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