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Problem doing induction question

  1. Oct 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove the following result using mathematical induction:
    2³+4³+6³+...+(2n)³=2n²(n+1)² for all n>or=1


    2. Relevant equations



    3. The attempt at a solution
    n=1:
    (2(1))³=2(1)²(2)³
    8=8

    Assume n=k
    2³+4³+6³+...+(2k)³=2k²(k+1)²

    n=k+1
    2³+4³+6³+...+(2k)³+(2(k+1))³=2(k+1)²(k+2)²
    Using assumption
    2k²(k+1)²+(2(k+1))³=2(k+1)²(k+2)²
    Divide by 2(k+1)²
    k²+k+1=(k+2)²
    k²+k+1=k²+4k+4

    I can't understand where I've gone wrong.
    Any help would be greatly appreciated.
     
  2. jcsd
  3. Oct 8, 2012 #2
    Figured it out the second I put it up. Removed a 2³ as a 2.
     
  4. Oct 8, 2012 #3

    SammyS

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    The following line looks as if you are assuming the very thing you are to prove.
     
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