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Algebra: Inequality

  1. Aug 9, 2016 #1
    hi! i need help for this inequality
    1. ##a\in\mathbb{N}*~and~ \frac{a}{a+1}<\frac{a+1}{a+2}<\frac{a+2}{a+3}##
    show that : ##\frac{1}{2}*\frac{4}{5}*...*\frac{2005}{2006}*\frac{2008}{2009}<\frac{1}{12}##

    Here i have stoped. Please tell me if is corect what i have done so far and how to continue , or another idea to solve
    salut.jpg
     
  2. jcsd
  3. Aug 9, 2016 #2

    pasmith

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    Use your inequality to obtain an upper bound for [itex]P_1^3[/itex].
     
  4. Aug 9, 2016 #3

    BvU

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    Hello Lizu, :welcome:

    Good start. Except the last factors: P1 last one is ##{2008\over 2009} ## etc.
    Make it so that your P1 is the product you are after
    You can still show ##\ \ P_1P_2 P_3 = {1\over 2011}\ \ ## and ##\ \ P_1<P_2<P_3 \ \ ##.

    So if you can show ##P_1^3 < P_1P_2P_3## you are in business !

    [edit] ah, PA was faster. Nice exercise !
     
  5. Aug 9, 2016 #4
    Thank you !!
     
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