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Find a formula for this sequence!

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A sequence (xj) where j can go from 0 to infinity satisfies the following:
    (1) x1= 1 and
    (2) for all m≥n≥0, xm+n+ xm-n= (1/2)(x2m+x2n)
    Find a formula for xj and prove that the formula is correct


    2. Relevant equations



    3. The attempt at a solution
    All I have done so far is is play around with m and n values so far and I think a proper formula:
    xj= j2. Now I would have to prove this (for which I plan to use induction most likely) but I wanted to see if I was on the write track in my thinking.
     
  2. jcsd
  3. Oct 11, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Looks fine to me. Now try and check it. Induction isn't really necessary. Just check that your guess works.
     
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