Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - 11.4 - Mathematical Induction - 11.4 Exercises - Page 806: 35


The property was proved for $n=1$ The property is correct if n is changed by $n+1$

Work Step by Step

Let's prove the property for $n=1$: $(ab)^n=(ab)^1=ab=a^1b^1$ It is correct! Suppose that the propety is correct, that is: $(ab)^n=a^nb^n$ for all integers $n\geq1$ Now, let's prove the property for $n+1$: $(ab)^{n+1}=(ab)^n(ab)^1=a^nb^nab=(a^na)(b^nb)=a^{n+1}b^{n+1}$ That is the given property if $n$ is changed by $n+1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.