Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Proof by induction
  1. Proof by induction (Replies: 6)

  2. Proof by induction (Replies: 8)

  3. Proof by Induction (Replies: 9)

  4. Induction Proof (Replies: 5)

  5. Induction Proof (Replies: 1)

Loading...