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Bernoulli Recursions

  1. Jan 10, 2008 #1
    I don't know if this is appropriate or not, here or anywhere. However, I propose this thread be used to post recursive formula for the Bernoulli numbers. It saves a great deal of frustration.
    The first is simply,

    [tex] \sum_{k = 0}^{n-1} \binom{n}{k} B_{k} = 0 [/tex]
  2. jcsd
  3. Jan 11, 2008 #2

    Gib Z

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    Homework Helper

  4. Jan 11, 2008 #3
    One of the first places I tried, maybe it'll be better if I'm a bit more specific- I need to show that,
    [tex] (1 - 2^{2k}) B_{2k} = \sum_{r = 1}^{k} B_{2(k-r)} \binom{2k}{2r} (2^{2(k-r) - 1} - 1) [/tex]
    (should be right...)
    Tried a few approaches, didn't work, I might not be trying hard enough(bit of a hectic period), I'd sure appreciate some help! A nod in the right direction even.
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