Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - Extention - Prove Statements Using Mathematical Induction - Practice - Page 837: 1


See below.

Work Step by Step

Proofs using mathematical induction consist of two steps: 1) The base case: here we prove that the statement holds for the first natural number. 2) The inductive step: assume the statement is true for some arbitrary natural number $n$ larger than the first natural number, then prove that the statement also holds for $n + 1$. Hence here: 1) For $n=1: 2(1)-1=1^2$. 2) Assume for $n=k: 1+3+...+2k-1=k^2$. Then for $n=k+1$: $1+3+...+2k-1+2k+1=k^2+2k+1=(k+1)^2.$ Thus we proved what we wanted to.
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.