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Math Help - Hi can somebody help me with induction pleaseeee

  1. #1
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    Hi can somebody help me with induction pleaseeee

    Hello,

    I heard from a friend that this forum is really good with helping me with discrete math.


    Prove n is less than 2^n by Induction

    So here's what I got so far, but i'm really not sure.

    Can somebody help me please!!! thanks

    for some S
    2<=n+1<S
    1<=n<S-1
    1<S-1<=2^n
    2<S<=2^n+1
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  2. #2
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    Quote Originally Posted by xeodox View Post
    Hello,

    I heard from a friend that this forum is really good with helping me with discrete math.


    Prove n is less than 2^n by Induction

    So here's what I got so far, but i'm really not sure.

    Can somebody help me please!!! thanks

    for some S
    2<=n+1<S
    1<=n<S-1
    1<S-1<=2^n
    2<S<=2^n+1
    1. True for n = 1.

    2. Assume true for n = k: k < 2^k is true.

    3. Show that true for n = k => true for n = k+1:

    k + 1 < 2^k + 1 < 2^k + 2^k = 2 (2^k) = 2^{k+1}.

    Therefore .......

    The finer details of the setting out are left for you.
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