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: 12


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 $n=1$: $3n(n+1)=3(1)(1+1)=3(2)=6$ It is correct! Now, suppose that the formula is correct, that is: $6+12+18+24+...+6n=3n(n+1)$ Now, let's prove the formula for $n+1$: $6+12+18+24+...+6n+6(n+1)=(6+12+18+24+...+6n)+6(n+1)=3n(n+1)+6(n+1)=(3n+6)(n+1)=3(n+2)(n+1)=3(n+1)(n+2)=3(n+1)[(n+1)+1]$ That is exactly the given formula if $n$ is changed by $n+1$.
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