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Math Help - factorial long division (or not?)

  1. #1
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    factorial long division (or not?)

    my textbook shows the result of n!/(n!+1) to be  \frac{1}{n+1}

    Does anyone know how they arrive at this result? Even wolfram shows something different.

    also latex is throwing errors whenever i use factorials.
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  2. #2
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    It's actually n!/(n + 1)! = 1/(n + 1). This is because (n + 1)! = (n + 1)n!.
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    Thanks. why is it equal to that? is this a rule for distributing factorials over parentheses? i have not seen that rule before.
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    It's because N! = N(N - 1)(N - 2)...(3)(2)(1) = N(N - 1)!.

    What happens if N = n+1?
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    should be N!= n+1(n)(n-1)(n-2)...(4)(3)(2)(1)=N+1(N)!
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    First of all, you MUST use brackets where they are necessary and second, N and n are different.

    It should be N! = (n + 1)(n)(n - 1)...(3)(2)(1) = (n + 1)n!.

    Therefore (n + 1)! = (n + 1)n!
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    Quote Originally Posted by skyd171 View Post
    Thanks. why is it equal to that? is this a rule for distributing factorials over parentheses? i have not seen that rule before.
    What you posted, , is not true if n\ne 1.

    It is true that
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  8. #8
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    Quote Originally Posted by Plato View Post
    What you posted, , is not true if n\ne 1.

    It is true that
    my math textbook is absurd, it does not mention that this relation is only true in a single scenario.
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  9. #9
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    Quote Originally Posted by skyd171 View Post
    my math textbook is absurd, it does not mention that this relation is only true in a single scenario.
    I am not sure how to read that.
    But the is true:
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