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Use mathematical induction to prove the following statements are true

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Use mathematical induction to prove the following statements are true for n≥1

    a) 1^2+3^2+5^2+...+(2n-1)^2= [n(4n-1)]/3

    2. Relevant equations



    3. The attempt at a solution
    Attempt at showing for n+1 is true:

    n[4(n+1-1)]/3+ 2[k+1-1)^2
     
  2. jcsd
  3. Sep 7, 2012 #2
    First off start by letting n=1 and check it. Then you can go to n+1.
     
  4. Sep 7, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    First, what you are trying to prove true is an equation, and you have not "=". It looks to me like this is the right side of n= k with the new term added- but there are several errors.
    First, bcause the term on the left is to be the "old" sum, you should not have "n+1" in place of n in 4(n-1)/3 but you should have 4(k-1)/3, not n. Second, in the sum the last term is (2n-1)^2- that is all squared so replacing n with k+ 1 gives (2(k+1)+1)^2 NOT "2[k+1-1]^2".

    Since you want to prove the original statement is true for all n, it is a good idea to use "k" and "k+1" for the induction step. But do not mix "k" and "n".
     
    Last edited: Sep 7, 2012
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