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Math Help - More help with induction!

  1. #1
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    More help with induction!

    I have no trouble with proving something by induction when I have a 'sum of' equation and an element equation, but I have no idea where to start with this:

    Show that m_n = 2^n - 1 by induction for all n \geq 1

    I have notes, but I can't make any sense out of them.

    Can someone help me out in understanding the process for this question?

    Cheers.
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  2. #2
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    Start with n = 1. Does it work?
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  3. #3
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    What m_n supposed to be?
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  4. #4
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    Okay, I'm an idiot. I missed some seriously crucial information and now I understand.
    This has been tripping me up for over an hour now -.- So simple.

    m_{n+1} = 2m_n + 1

    Show that m_n = 2^n - 1 by induction for all n \geq 1

    n = 1 : m_n = 2^n - 1 = 1
    m_{n+1} = 2m_n + 1
    m_{n+1} = 2(2^n - 1) + 1
    m_{n+1} = 2^{n+1} - 1

    Cheers guys.
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