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10-75.
  1. Examine Kari’s proof by induction below. Homework Help ✎

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

    3 + 6 + 9 + … + 3k + 3(k + 1)

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

    =k2 + k + 3k + 3

    =k2 + k + 3

    =(k2 + 3k + 2)

    =(k + 1)(k + 2)

    Therefore, the relationship is true for n = k + 1 whenever it is true for n = k.

    1. What did she prove?

    2. 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?