Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.4 - Mathematical Induction - Concept and Vocabulary Check - Page 1084: 1


The principle of mathematical induction states that a statement involving positive integers is true for all positive integers when two conditions have been satisfied: The first condition states that the statement is true for the positive integer $1$. The second condition states that if the statement is true for some positive integer $ k $, it is also true for the next positive integer $ k+1$.

Work Step by Step

We know that the principle of mathematical induction is as follows: Assume ${{S}_{n}}$ to be a statement involving the positive integer $ n $. If (1) ${{S}_{1}}$ is true and (2) The truth of the statement ${{S}_{k}}$ implies the truth of the statement ${{S}_{k+1}}$, for every positive integer $ k $. Then we can prove the statement ${{S}_{n}}$ is true for all positive integers $ n $ .
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.