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Math Help - Sequence proof

  1. #1
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    Sequence proof

    I need help with the following proof:

    Let  (x_{n})_{n} be a sequence of real numbers such that  x_{n} + x_{n+1} converges and x_{n}x_{n+1} converges. Show that (x_{2n}) converges
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Well clearly then a_n = x_{2n}+x_{2n+1} and b_n = x_{2n}x_{2n+1} converge. Therefore \frac{a_n\pm\sqrt{a_n^2-4b_n}}{2} = \{x_{2n},x_{2n+1}\} both converge.
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  3. #3
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    why is it that we can just pass it though the quadratic formula?
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