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Proof by induction

  1. May 9, 2007 #1
    Sum from r=1 to n (3r+1) = n/2(3n+5)


    Prove true for n=1:
    3*1+1=4 | 1/2(3*1+5)=4



    Assume true for n=k:
    k/2(3k+5)


    Prove true for n=(k+1):
    k/2(3k+5) + (3(k+1)+1) | 1/2(k+1)(3(k+1)+5)
    k/2(3k+5) + (3k+3+1) | 1/2(k+1)(3k+3+5)
    k/2(3k+5) + (3k+4) | 1/2(k+1)(3k+8)


    now what? I can't see what factors I can take out of either to make them the same... any ideas?


    EDIT: nevermind:

    1/2(3k^2+5k+2(3k+4) | 1/2(k+1)(3k+8)
    1/2(3k^2+11k+8) | 1/2(k+1)(3k+8)
    1/2(k+1)(3k+8) | 1/2(k+1)(3k+8)


    Same, therefore proved by induction.


    :D
     
    Last edited: May 9, 2007
  2. jcsd
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