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Math Help - Showing a sequence tends to infinity

  1. #1
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    Showing a sequence tends to infinity

    Define a sequence recursively by a_{n+1} = 2a_{n}^2.

    Given a_{0} > 1/2, show lim a_{n} = \infty.

    Note: It can easily be shown that a_{n} > 1/2 so just assume this is given.
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  2. #2
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    Let b_n=2 a_n .
    We have the following reccurence for sequence b_n:
    <br />
b_{n+1}=b_n^2<br />
    But for this sequence explicit formula can be easily obtained:
    <br />
b_n=b_0^{2^n}<br />
    Because  b_0 > 1 the sequence is not convergent.
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  3. #3
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    Hey, sorry for the late response, thanks though.

    So I can just assume b_{n} > 1/2 and just say since,

    b_{n} < a_{n} for all n?
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