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Math Help - Induction Help

  1. #1
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    Induction Help

    Im trying solve 2 questions using induction.

    Problem 1.

    n equals 2^n where n is length of bit string (For example if n = 1, then only 0 and 1 are possible outcomes).

    Base Case: Assume n = 1, therefore 2^1 = 2. Which is correct as i described above.

    Induction Case: I get alittle troubled by something now..
    Show that P(n) holds then so does P(n+1).

    n, (n+1) = 2^(n+1)
    Now I rearrange the RHS correct?
    = (2n + 2)
    =2(n+1)

    Can somebody help me out if im on the right track on this?


    Problem 2.
    Similar problem but the numbers of binary words of length at most n is equal to 2^(n+1) - 1.
    Base Case: n = 1
    So 2^(1+1)-1 = 3
    Shouldnt it be 2?


    I know that both of these are correct i just have to prove them, but my mind gets muddled as i described above and id love some clarification if possible.
    (Actually it could be that i need to prove them false).

    Thanks for giving me your generous help.
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  2. #2
    MHF Contributor

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    I have no idea what you think the problem actually says.
    BUT \left( {\forall n \in \mathbb{N}} \right)\left[ {{\color{red}n \ne 2^n} } \right].

    Why don't you quote the problem exactly as it was given to you?
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  3. #3
    Junior Member
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    Sorry, whats clear to me isnt always clear to someone else i suppose!

    Problem 1: I need to use induction to prove that the number of binary strings of length n equals 2^n.

    Problem 2.Number of binary strings of length at most n equals 2^(n+1) -1
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