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Math Help - Power of 5

  1. #1
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    Power of 5

    What is the power of 5 in

    (1!*2!......10!)*(1!*2!.....100!)*(1!*2!.....1000! )
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  2. #2
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    Quote Originally Posted by itsmaximhere View Post
    What is the power of 5 in

    (1!*2!......10!)*(1!*2!.....100!)*(1!*2!.....1000! )
    Analyze the number of factor 5 in the brackets:

    (1!*2!......10!) contains 5^6

    (1!*2!.....100!) contains 5^{96} \cdot (5^2)^{76}

    (1!*2!.....1000!) contains 5^{996} \cdot (5^2)^{976} \cdot (5^3)^{876} \cdot (5^4)^{376}

    Not sure about the last line so check my arithmetic, please!
    Last edited by earboth; December 2nd 2009 at 10:47 PM. Reason: typo
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