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Math Help - Need some help with induction

  1. #1
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    Need some help with induction

    Hi guys was just wondering if anyone could help me out with this
    Use induction to prove
    20 + 21 + 22 ... +2n = 2n+1 ​-2
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  2. #2
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    Re: Need some help with induction

    What did you try ?
    Thanks from topsquark
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  3. #3
    MHF Contributor

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    Re: Need some help with induction

    Presumably you know what "induction" is! First prove the general statement for the specific case n= 0. Is 2^0= 2^{0+1}- 2?

    Then assume it true for some specific (but indeterminate) number, say n= k. That is your "induction hypothesis[/tex] is 2^0+ 2^1+ \cdot\cdot\cdot+ 2^k= 2^{k+1}- 2. Now you need to use that to show that it is also true when n= k+1. Okay, 2^0+ 2^1+ \cdot\cdot\cdot+ 2^{k+1}= (2^0+ 2^1+ \cdot\cdot\cdot+ 2^k)+ 2^{k+1}.

    Can you apply your induction hypothesis to that?
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