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Math Help - [SOLVED] Factorial series question

  1. #1
    Senior Member mollymcf2009's Avatar
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    [SOLVED] Factorial series question

    Please see the attached problem:

    factorial series.pdf

    My question is, what happened to the k! in the top when the original series is simplified? How does that get canceled?
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Please see the attached problem:

    factorial series.pdf

    My question is, what happened to the k! in the top when the original series is simplified? How does that get canceled?
    \frac{k!}{(k+3)!} = \frac{k!}{(k+3)(k+2)(k+1) \cdot k!}

    so ... what happened to the k! ?
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  3. #3
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    Alright, so, two things,

    k! = (k)(k-1)(k-2)(k-3)(k-4)(k-5)...etc

    (k+3)! = (k+3)(k+3-1)(k+3-2)(k+3-3)(k+3-4)(k+3-5)

    now you'll notice that, simplifying, (k+3-3) = k, and (k+3-4) = (k-1), and (k+3-5) = (k-2), etc.

    so in effect, (k+3)! has all of the terms as k!, with the except of the first three terms of (k+3)!, so you can divide them out

    hopefully that explains it well enough. if not lemme know
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