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Math Help - Having trouble with induction proof and limit

  1. #1
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    Having trouble with induction proof and limit

    Can someone just show me a full blown proof of this problem, I really would have posted everything I had, but its really hard for me to type everything I had. Thanks

    Let 0< a1< b1 and define

    an+1= √anbn

    bn+1=(an+bn)/2


    a) Use induction to show that
    an<an+1<bn+1<bn

    Thus prove that an and bn converge.
    b) Prove that they have the same limit.


    This is what I got so far

    1) show it's true for n=1 first.
    I derived these an+1=square root of anbn>square root of anan =an


    an<an+bn/2<bnanan=an => an<bn+1<bn

    I couldn't derive anything for the second term
    Last edited by Swamifez; December 21st 2006 at 03:27 AM.
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