### Home > INT3 > Chapter 10 > Lesson 10.1.5 > Problem 10-75

10-75.

Examine Kari’s proof by induction below. Homework Help ✎

I know 3 + 6 + 9 + … + 3

*n*=*n*(*n*+ 1) is true for*n*= 2 because 3 + 6 =(2)(2 + 1) = 9. If I assume that 3 + 6 + 9 + … + 3 *k*=*k*(*k*+ 1) is true, then:3 + 6 + 9 + … + 3

*k*+ 3(*k*+ 1)=

*k*(*k*+ 1) + 3(*k*+ 1)=

*k*^{2}+*k*+ 3*k*+ 3=

*k*^{2}+*k*+ 3=

( *k*^{2}+ 3*k*+ 2)=

( *k*+ 1)(*k*+ 2)Therefore, the relationship is true for

*n*=*k*+ 1 whenever it is true for*n*=*k.*What did she prove?

How could she adjust her proof so that she can know for sure that the relationship is true for all

*n*≥ 1?

What is the relationship? When (for what numbers) is it true?

Which value of *n* should she check instead of the one she did?