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Math Help - Limit question

  1. #1
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    Limit question

    Show that this converges and where it converges too.

    a(n+1) = 1/2(an +3/an). given that (a1=2)

    Well I found out where it converges too by starting with a1=2 that gave me a2 = 7/4, a3 = 97/56 and that is very close too sqrt:3 so that is where it goes. .
    I am however not sure how to "show" that it converges...?
    A general hint on how to show anything here is fine I really wan´t too solve these by myself...
    Last edited by Henryt999; January 29th 2010 at 06:49 AM.
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  2. #2
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    Quote Originally Posted by Henryt999 View Post
    Show that this converges and where it converges too.

    a(n+1) = 1/2(an +3/an). given that (a1=2)

    Well I found out where it converges too by starting with a1=2 that gave me a2 = 7/4, a3 = 97/56 and that is very close too sqrt:3 so that is where it goes. .
    I am however not sure how to "show" that it converges...?
    A general hint on how to show anything here is fine I really wan´t too solve these by myself...
    Do you the mathematical induction?
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  3. #3
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    Exactly what?

    We might have another name for it in europe? "there is something called the inductionaxiom but I am not suppose to use that here..
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  4. #4
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    Acctually let me refrase the question.

    I have to show that it converges. Well I can do that by putting numbers in.
    But I can only show that it converges from the left to sqrt3.
    Any tips on how I can show that it also converges from the right?
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  5. #5
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    Quote Originally Posted by Henryt999 View Post
    Show that this converges and where it converges too.

    a(n+1) = 1/2(an +3/an). given that (a1=2)

    Well I found out where it converges too by starting with a1=2 that gave me a2 = 7/4, a3 = 97/56 and that is very close too sqrt:3 so that is where it goes. .
    I am however not sure how to "show" that it converges...?
    A general hint on how to show anything here is fine I really wan´t too solve these by myself...
    Do you mean

    a_{n+1} = \frac{1}{2} \left(a_n + \frac{3}{a_n}\right), given that a_1=2 ?

    You have found \sqrt{3} as a possible limit. Now you need to use induction to show that 0 < a_{n+1} < a_n for all n greater than 1.
    Last edited by mr fantastic; January 29th 2010 at 02:08 PM.
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