College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Concept and Vocabulary Check - Page 750: 3


See below.

Work Step by Step

By substituting in: for $n=3$: $3+7+11=3(6+1)$ for $n=k+1$, before simplication: $3+7+11+...+(4(k+1)-1)=(k+1)(2(k+1)+1)$, which is equivalent to: $3+7+11+...+(4k+3)=(k+1)(2k+3)$,
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