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Finding limit

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

    where 0<x<y
    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


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    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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