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Mathematical Induction (The inductive step)

  1. Dec 13, 2011 #1
    1. I don't understand how to prove this.
    for all n≥1, 10n - 1 is divisible by 9.





    3. I've done the basis step.
    Now i'm on the inductive step.
    I'm using (10k+1-1)/9=1.
    I don't know where to go from there.
    Using algebra just gets me down to 10k+1= 10. And I really don't think that's the answer.
    All examples i've seen show me things like 1...2..3..n+1= n(n+1) or something along the lines. They already give me the equation. This one does not.
     
    Last edited by a moderator: Dec 13, 2011
  2. jcsd
  3. Dec 13, 2011 #2

    Mark44

    Staff: Mentor

    This isn't right. You need to show that 10k+1-1 is divisible by 9, not that it is equal to 9. There is a difference. For example, 27 is divisible by 9, but the two numbers aren't equal.
    What do you have for your induction hypothesis?
     
  4. Dec 13, 2011 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Assume that 10k-1 is divisable by 9. Prove that it implies 10k+1-1 is also divisable by 9.

    Try to bring 10k+1-1 to such form that it contain 10k-1.
    10k+1=10*10k=> 10k+1-1=10*10k-1=10*10k-10+10-1=
    10(10k-1)+9.
    Can you proceed from here?


    ehild
     
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