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Math Help - inequality

  1. #1
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    Smile inequality

    Hi everyone,
    Can you help me to prove that
    (1-b^(m+1))(-(b+1))/b^2<(1+b+b^2+b^3+...+b^m)
    in logestic way

    If you can try to answer me today because I have exam tomorrow in it

    Thanks for any helping
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rosana View Post
    Hi everyone,
    Can you help me to prove that
    (1-b^(m+1))(-(b+1))/b^2<(1+b+b^2+b^3+...+b^m)
    in logestic way

    If you can try to answer me today because I have exam tomorrow in it

    Thanks for any helping
    i'd probably try induction. did you learn mathemtical induction?
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  3. #3
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    Quote Originally Posted by rosana View Post
    Hi everyone,
    Can you help me to prove that
    (1-b^(m+1))(-(b+1))/b^2<(1+b+b^2+b^3+...+b^m)
    in logestic way

    If you can try to answer me today because I have exam tomorrow in it

    Thanks for any helping
    Do you mean, for b\not =0:
     \frac{(1-b^{m+1})(-(b+1))}{b^2} < 1+b+b^2+...b^m
    Note that if b=1 then it is trivial.
    Assume that b\not = 1 then:
    \frac{(1-b^{m+1})(-(b+1))}{b^2} < \frac{1-b^{m+1}}{1-b}
    If |b|<1 then 1-b^{m+1}>0 and hence:
    \frac{-(b+1)}{b^2} < \frac{1}{1-b}
    Which is true because LHS is negative and RHS is positive.
    If |b|>1 then 1-b^{m+1}<0 and hence*:
    \frac{-(b+1)}{b^2} > \frac{1}{1-b}
    Thus,
    (b+1)(b-1) < b^2
    Thus,
    b^2 - 1 < b^2
    Which is true.


    *)It also depends when m is even or odd, but those a minor details.
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  4. #4
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    analysis

    it need analysis from us
    we know that (1+b+b^2+b^3+...+b^m)=(1-b^(m+1))/(1-b)
    but how to use it

    think for me please
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  5. #5
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    Quote Originally Posted by rosana View Post
    it need analysis from us
    we know that (1+b+b^2+b^3+...+b^m)=(1-b^(m+1))/(1-b)
    but how to use it

    think for me please
    This is the Geometric Sum.
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  6. #6
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    thanks

    thaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaanks so much Perfect Hackers

    I believe that you can answer any thing because you are genios and fantastic guy


    thanks again you help me and now I can get full mark in final exam in mathematical analysis
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  7. #7
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    Quote Originally Posted by rosana View Post
    you are genios
    I know
    and fantastic guy
    I am the greatest. The world shall bow before my will.
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    The world shall bow before my will.
    Wow. My will merely states that I'm of sound mind and body. (Hard to believe, I know!) Can you send me a copy of your will so I can see how you do that?

    -Dan
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