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Thread: Sequence Question

  1. #1
    Junior Member
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    Sequence Question

    We define a sequence recursively in the following way.

    $\displaystyle s_1=2$

    and

    $\displaystyle s_n=\sqrt{3+2_{s_{n-1}}}$ for $\displaystyle n>1$

    1. Show that $\displaystyle {s_n}$ is an increasing sequence.
    2. show that $\displaystyle {s_n}$ is bounded from above
    3.Compute $\displaystyle \lim_{n\rightarrow \infty} $ of $\displaystyle s_n$
    Last edited by jpatrie; Oct 14th 2008 at 10:10 AM.
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  2. #2
    MHF Contributor

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    Do this by induction.
    $\displaystyle s_K < s_{K + 1} \Rightarrow \quad s_{K + 1} < s_{K + 2}
    $
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