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Double Factorial

  1. Oct 14, 2011 #1
    How to prove


    for example





    I see that by intiution but I don't know how to write prove.
  2. jcsd
  3. Oct 14, 2011 #2


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    Prove it by induction. You've shown that it holds for the case n =1, so if you assume that it holds for general n, show that it follows that it holds for the case n+1.
  4. Oct 14, 2011 #3


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    You don't need induction. A direct computation using the definition of the double factorial is enough.
  5. Oct 14, 2011 #4
  6. Oct 14, 2011 #5
    (2 n)!! = 2 \times 4 \times \ldots \times (2 n)

    But, notice that:
    2 = 2 \times 1 \\

    4 = 2 \times 2 \\

    \ldots \\

    2 n = 2 \times n

    Combine the first factor of two from each factor in the double factoriel. How many of them are there? What do the remaining factors give?
  7. Oct 14, 2011 #6
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