Results 1 to 9 of 9

Math Help - general math problems

  1. #1
    Newbie
    Joined
    Sep 2006
    Posts
    9

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,933
    Thanks
    336
    Awards
    1
    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
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2006
    Posts
    9

    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
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    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.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2006
    Posts
    9
    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!!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    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.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Sep 2006
    Posts
    9
    i don't understand what u said, how did u come up with the answer? and what does pi have to do with this ?!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. general random variables problems
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 6th 2010, 04:41 AM
  2. General math website
    Posted in the Math Forum
    Replies: 0
    Last Post: September 16th 2009, 04:22 PM
  3. General Math Questions, exponents
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: January 21st 2009, 02:14 AM
  4. General Discrete Math Help
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 9th 2007, 01:00 AM
  5. general math number theory
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 18th 2006, 10:00 AM

Search Tags


/mathhelpforum @mathhelpforum