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Proof by induction, puzzles by answer

  1. Jun 6, 2012 #1
    Ok, so there's this proof by induction question. I looked at the answer for it but I don't understand it.

    TuXle.jpg

    How does it get from being 2^(k+1) to being 2^(k+2)?
     
    Last edited by a moderator: Jun 6, 2012
  2. jcsd
  3. Jun 6, 2012 #2
    You need to provide a little more background into your question, I think.
     
  4. Jun 6, 2012 #3

    HallsofIvy

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    Your image did not link properly so it is impossible to answer your question.
     
  5. Jun 6, 2012 #4

    D H

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    [itex]2^{k+1}(k-1+k+1) = 2^{k+1}(2k) = 2^{k+2}k[/itex]
     
  6. Jun 11, 2012 #5
    you got [2^(k+1)](2k).

    multiply 2^(k+1) by two, that is raising your exponent by 1. Hence 2^(k+2)
     
    Last edited: Jun 11, 2012
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