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Math Help - Simplifying Expression with Like Denominators and Factorials

  1. #1
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    Simplifying Expression with Like Denominators and Factorials

    Hi,

    I am having difficulties simplifying the expression  \frac{1}{k!}-\frac{1}{(k+1)!} .

    To obtain like denominators,  \frac{1}{k!}-\frac{1}{(k+1)!}=\frac{(k+1)!-k!}{k!(k+1)!} , but I do not know how to further simplify the expression. The factorials are messing with me, I think.

    Any help would be most certainly appreciated!

    Cheers!
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  2. #2
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    Re: Simplifying Expression with Like Denominators and Factorials

    Answered in this thread.
    Thanks from topsquark
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  3. #3
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    Re: Simplifying Expression with Like Denominators and Factorials

    Hello, SC313!

    \text{Simplify: }\:\frac{1}{k!}-\frac{1}{(k+1)!}

    Multiply the first fraction by \frac{k+1}{k+1}

    . . \frac{1}{k!}\cdot\frac{k+1}{k+1} - \frac{1}{(k+1)!} \;=\;\frac{k+1}{(k+1)!} - \frac{1}{(k+1)!} \;=\;\frac{(k+1) - 1}{(k+1)!} \;=\;\frac{k}{(k+1)!}
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  4. #4
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    Re: Simplifying Expression with Like Denominators and Factorials

    Simplifying Expression with Like Denominators and Factorials-02-nov-13.png
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