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Math Help - Induction for an inequality

  1. #1
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    Induction for an inequality

    could some one help please
    let a1=2

    an+1=3+an^2/2an

    prove n>=1 an>root3
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  2. #2
    Member
    Joined
    Mar 2009
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    hmmm... this is an interesting question, but I'm not sure if I've understood it correctly. Do you mean:
    <br />
a_{n + 1} = (\frac{3 + a_n^2}{2a_n}) ;  n > 1, a_n > \sqrt{3}<br />
?

    Oops, took me a while to figure out what was meant by the question...

    <br />
a_{n + 1} = \frac{3 + (\sqrt{3})^2}{2(\sqrt{3})} = \frac{3}{\sqrt{3}} =\sqrt{3} ; substitue a_n = \sqrt{3}

    mind you that's not an answer!
    Last edited by bmp05; February 6th 2010 at 12:05 AM.
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