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Putnam 1999 a3

  1. Nov 7, 2007 #1
    1. The problem statement, all variables and given/known data
    In the first solution to 1999 A3 at the this website:
    http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1999s.pdf [Broken]

    You do not need to read the problem.

    I do not see hot they go the recurrence relation in the first sentence. Specifically I do not follow reason why their first expression "yields the recurrence..."?




    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Nov 7, 2007 #2

    Hurkyl

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    Did you try multiplying it out and collecting like terms?
     
  4. Nov 7, 2007 #3
    Yes. But you still have that one on the other side. I do not know what to do with that.
     
  5. Nov 7, 2007 #4

    Hurkyl

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    I'm not sure what you mean. You have an equation; the two sides are equal.
     
  6. Nov 7, 2007 #5
    I am saying the 1 is outside of the summation. I need to have everything in a summation before I can get the desired result, don't I?
     
  7. Nov 7, 2007 #6

    Hurkyl

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    Both sides of the equation are power series. What has to be true for two power series to be equal?
     
  8. Nov 9, 2007 #7
    I see. The coefficients of all powers of x greater than 0 must b 0 and the coefficient of x^0 must be 1.
     
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