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: 11

Answer

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

Work Step by Step

Let's prove the formula for $n=1$: $n(n+1)=1(1+1)=1(2)=2$ It is correct! Now, suppose that the formula is correct, that is: $2+4+6+...+2n=n(n+1)$ Now, let's prove the formula for $n+1$: $2+4+6+...+2n+2(n+1)=(2+4+6+...+2n)+2(n+1)=n(n+1)+2(n+1)=(n+2)(n+1)=(n+1)(n+2)=(n+1)[(n+1)+1]$ That is exactly the given formula 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.