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Math Help - Can the series (k!)/(1x2x3...(2k-1)) be written as the series (k!)/(2k-1)!?

  1. #1
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    Can the series (k!)/(1x2x3...(2k-1)) be written as the series (k!)/(2k-1)!?

    It was a question on one of my exams and I think my TA graded it wrongly because he wrote that:

    \sum \frac {k!}{1x2x3...(2k-1)} = \sum \frac {k!}{(2k-1)!}

    I disagree, but can someone explain it?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by chrozer View Post
    It was a question on one of my exams and I think my TA graded it wrongly because he wrote that:

    \sum \frac {k!}{1x2x3...(2k-1)} = \sum \frac {k!}{(2k-1)!}

    I disagree, but can someone explain it?
    I assume those x's refer to multiplication?

    Well it seems as if you're multiplying consecutive integers in that denominator, and by definition n!=n(n-1)(n-2)\cdots 3\cdot 2\cdot 1. Thus, we can say that 1\cdot2\cdot3\cdots(2k-1)=(2k-1)!.

    Does this clarify things?
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  3. #3
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    Yes it does. Thanks alot. I had it confused with something else.
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