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Homework Help: Direct formula derived from recursive formula

  1. Feb 19, 2010 #1
    1. The problem statement, all variables and given/known data
    I have a recursive formula and I'm trying to find a direct formula.

    2. Relevant equations
    The recursive formula: T(n) = T(n-2) + n^2

    No base is given. The question says "Assume that T(n) is constant for n <- 2

    3. The attempt at a solution
    T(1) = 0
    difference: 4
    T(2) = 4
    difference: 6
    T(3) = 10
    difference: 8
    T(4) = 18
    difference: 10
    T(5) = 28

    So the difference is 2n, but then I get stuck and don't know how to go further and get a direct formula.
  2. jcsd
  3. Feb 19, 2010 #2
    Do you know the explicit formula for [tex]1 + 2 + \dots + n[/tex]? It will help you solve this problem, and it's something you should know anyway. (Hint: fold the sequence in the middle.)
  4. Feb 19, 2010 #3
    The sum from k=0 to n of s+kv = (n+1) s + 1/2 n(n+1)v

    But I don't know what to do because the difference doesn't start with 2
  5. Feb 19, 2010 #4
    Imagine it did, then correct for the problem afterward!
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