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Mathematical Induction

  1. Oct 17, 2006 #1
    ok I am really confused now topic says it all..

    I am given 4n-3 = n(2n-1)

    using mathemadical induction proof that is true.

    P(1) both equal 1

    P(k) 4k-3 = k(2k-1)
    = k^2 - k

    P(k+1) 4(k+1)-3 =(k+1)(2(k+1)-1)

    if i simplify it all i get that
    4k +1=2k^2 +3k +1

    but stick at that point.

    any help plz.
  2. jcsd
  3. Oct 17, 2006 #2


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    The proposition 4n-3 = n(2n-1) for all natural numbers is false; no wonder you can't prove it. Take n=5 for exemple. It would then say that 17=45
  4. Oct 17, 2006 #3
    hmm....did u miss out the summation sign on the left side?
  5. Oct 17, 2006 #4
    kay here is the exact question from the text.


    so how do i do this then...
  6. Oct 17, 2006 #5
    You do realise that it's not the same as what you said in the first post?

    Assuming it's true for some k, add 4(k+1)-3 to the left and try to simplify it so that you get the corresponding term for k+1 on the right.
  7. Oct 17, 2006 #6
    (4n-3) is not summation (4n-3) :rofl: sub n=k+1 on the right and proof that its equal to k(2k-1) + (k+1)th term. i guess it should be alrite from here :biggrin:
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