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(1+1/n)^n problem

  1. Jan 29, 2006 #1

    MathematicalPhysicist

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    it's rather a bypass question, not a direct question about 'e'.

    the last term in the binomial expansion of (1+1/n)^n is according to my text:
    (1/n!)(1-1/n)(1-2/n)....(1-(n-1)/n)
    while it should be (1/n!)(n(n-1)...1)/n^n

    okay, these two terms are almost identical, the first equals
    (with disregarding of 1/n!):
    ((n-1)(n-2)...1)/n^n
    and second one is the first multiplied by n, then what is the problem.

    i assume it's with me ( just kidding).
     
  2. jcsd
  3. Jan 29, 2006 #2

    benorin

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    (1/n!)(1-1/n)(1-2/n)....(1-(n-1)/n)
    = (1/n!)(n-1)(n-2)....(n-(n-1))/n^(n-1)
    = (1/n!)(n-1)...1/n^(n-1)
    = (1/n!)(n(n-1)...1)/n^n

    so, they're the same
     
  4. Jan 29, 2006 #3

    MathematicalPhysicist

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    okay i think i can see it, thanks.
     
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