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Finding limit

  1. Dec 9, 2004 #1
    Sequences a_n and b_n are defined in the follwing way:

    a_1=x;
    b_1=y;
    where 0<x<y
    and:
    a_(n+1) = (a_n+b_n)/2
    b_(n+1) = sqrt(a_(n+1)+b_n)

    Proof, that both sequences are convergent to the same limit and find this limit.

    Thanks a lot for any help.
     
  2. jcsd
  3. Dec 9, 2004 #2

    AKG

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    Science Advisor
    Homework Helper

    You should be able to isolate and rearrange a bunch of times so that you get a_(n+1) and b_(n+1) in terms of a_n and b_n. See what you can do from there.
     
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