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Math Help - what is the remainder of the summation when divided by ten

  1. #1
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    what is the remainder of the summation when divided by ten

    I got this question in a maths competition. the question was that what was the remainder of the equation given below when divided by 10.

    \sum_{n=1}^{10} (n^2+3n+1)n!

    i personally do not what to do with the n!
    im lost
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  2. #2
    Senior Member Dinkydoe's Avatar
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    Hee swanz,

    Do you know how to do modulo-calculations? That is, how to add and multiply residu-classes modulo 10?

    This problem is actually quite simple if you can do this and make one simple observation. Namely, n!\equiv 0 mod 10 for all n\geq 5
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  3. #3
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    Start by noting that for any n \geq 5, ~ n! \equiv 0 ~ (mod 10).

    Ah, Dinkydoe got to it before I did... !
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  4. #4
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    no i am in kindda in high school still lol
    sorry =/ but u can tell me whateva i need to learn to solve this thereby i can learn some of it online,
    yes i knw n! mod 10 = 0
    yes i did make that observation that n! in mod 10 is 0 for all values of n more than equal to 5...but still lost :L
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  5. #5
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    sorry ....i got it :L ...
    i just thought there wud be a method going about this :L
    thanx for the insight Defunkt and Dinkydoe
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  6. #6
    Senior Member Dinkydoe's Avatar
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    Do you actually know that insight has the following implication?

    \sum_{n=1}^{10}(n^2+3n+1)n! has the same remainder as \sum_{n=1}^{4}(n^2+3n+1)n! when divided by 10
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  7. #7
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    yup got that bit ....dunno wat hppned b4... brain freezed i guess :L
    thanx a bunch Dinkydoe
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