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Math Help - convergent

  1. #1
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    convergent

    show \ that \ the \ sequence :
    x_1=3 \ , \ x_{n+1}= \frac{x_n}{2}+ \frac{4}{x_n}
    is \ convergent \ and \ find  \ its \ limit?
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  2. #2
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    The same, prove that is a monotone bounded sequence.

    Besides x_n is a subsequence of x_{n+1}, so both sequences converge to the same limit (which you need to prove that exists, so call it l), then the limit is l=\frac l2+\frac4l.
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