Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 5 - Sequences, Mathematical Induction, and Recursion - Exercise Set 5.3 - Page 267: 37

Answer

See below.

Work Step by Step

Use proof by contradiction: suppose not, that is "there are no three successive integers whose sum is at least 45." Divide the numbers into groups of threes, there will be a total of 10 groups with a total sum $S\lt 10(45)=450$ As we know the sequence is from 1 to 30, we can calculate the sum using a formula: $S(30)=\frac{30}{2}(1+30)=465\gt450$ Thus we have a contradiction and we can conclude that the original statement is true.
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