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Prove that recurrence relation is odd

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Hello!

    I just want to be sure if I did solve the task correctly.

    The task is:

    Prove that bn is odd for integers n>=1

    b1=1
    b2=3
    bk=bk-2+2bk-1 for k>=3


    2. Relevant equations


    3. The attempt at a solution

    Induction basis:

    b1=1 true 1 is odd
    b2=3 true 2 is odd

    Now the question is:

    Could I use the strong (complete) induction?

    If I can use it, the solution is simple:

    Let the recurrence relation is true for all k, such that n<k and n=k i.e n<=k
    bk=bk-2+2bk-1

    then for n=k+1

    bk+1=bk-1+2bk

    bk-1 is odd and 2bk is even therefore odd+even=odd

    Is this correct?

    Thank you.

    Regards.
     
  2. jcsd
  3. Sep 13, 2011 #2
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