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Math Help - general math problems

  1. #1
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    general math problems

    hey hey,
    i'm very new in here!!and i got a prob, actually two :
    1. prove that any sum of more than 7 cents can be made up out of 3 cents and 5cents coins.
    2.using mathematical induction, prove that for all n>1 the following inequality holds: 1/2squert + 1/3squert + .......+ 1/nsquert <1
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  2. #2
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    Quote Originally Posted by yaszine View Post
    hey hey,
    i'm very new in here!!and i got a prob, actually two :
    1. prove that any sum of more than 7 cents can be made up out of 3 cents and 5cents coins.
    I am not going to post a proof of this, (I once did on this forum maybe I can find it).
    But the result you can use is Sylvester's Coin Problem.
    In this case,
    (3)(5)-(3)-(5)=15-8=7
    ---
    I do not understand the second question.
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  3. #3
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    Quote Originally Posted by yaszine View Post
    Using mathematical induction, prove that for all n>1 the following inequality holds: 1/2squert + 1/3squert + .......+ 1/nsquert <1
    The only thing I can think of here is that you mean:
    1/sqrt(2) + 1/sqrt(3) +....+1/sqrt(n) < 1

    However 1/sqrt(2) + 1/sqrt(3) = 1.28445705

    -Dan
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    Quote Originally Posted by topsquark View Post
    The only thing I can think of here is that you mean:
    1/sqrt(2) + 1/sqrt(3) +....+1/sqrt(n) < 1

    However 1/sqrt(2) + 1/sqrt(3) = 1.28445705

    -Dan
    Also, this sequence is the zeta function for x=1/2
    Which by the integral test diverges, it much exceeds all numbers.
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  5. #5
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    here's the problem

    This is what i meant : 1 /(2 to the power 2) + 1/(3 to the power 2) + 1/(4 to the power 2) ………..+1/(nto the power two 2) < 1 !! i don't think it can ever be bigger than 1
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    Quote Originally Posted by yaszine View Post
    This is what i meant : 1 /(2 to the power 2) + 1/(3 to the power 2) + 1/(4 to the power 2) ..+1/(nto the power two 2) < 1 !! i don't think it can ever be bigger than 1
    Here is the cowardly way of doing it.
    The least upper bound for this series is,
    pi^2/6-1<1
    Thus, the partial sums must all be less than 1.
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  7. #7
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    the thing is for my second question is to prove that the sum in the left is less or equal to 1 - 1/n !! but i don't know how !
    for the first question, i couldn't see anyway i could solve it with that guy's coins' theory!!
    anyways, thanks alot for help ! the hw is due tomorrow!! i'll scratch my head and see if i can solve it by midnight ! otherwise ...
    thanks again!!
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  8. #8
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    Quote Originally Posted by yaszine View Post
    the thing is for my second question is to prove that the sum in the left is less or equal to 1 - 1/n !! but i don't know how !
    for the first question, i couldn't see anyway i could solve it with that guy's coins' theory!!
    anyways, thanks alot for help ! the hw is due tomorrow!! i'll scratch my head and see if i can solve it by midnight ! otherwise ...
    thanks again!!
    Tell your professor what I said. He will be proud of you, maybe give you extra credit.
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  9. #9
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    i don't understand what u said, how did u come up with the answer? and what does pi have to do with this ?!!
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