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Thread: Analysis: Sequences

  1. November 16th 2008, 02:36 PM #1
    GoldendoodleMom
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    Analysis: Sequences

    Suppose lim Sn = S with S > 0.. Prove that there exists a real number N such that Sn > 0 for all natural numbers n.
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  2. November 16th 2008, 02:43 PM #2
    Plato
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    Quote Originally Posted by GoldendoodleMom View Post
    Suppose lim Sn = S with S > 0.. Prove that there exists a real number N such that Sn > 0 for all natural numbers n.
    \begin{gathered}<br /> S > 0 \Rightarrow \quad \frac{S}<br /> {2} > 0 \hfill \\<br /> \left( {\exists N} \right)\left[ {n \geqslant N \Rightarrow \quad \left| {s_n - S} \right| < \frac{S}<br /> {2}} \right] \hfill \\<br /> - \frac{S}<br /> {2} < s_n - S < \frac{S}<br /> {2} \Rightarrow \quad 0 < \frac{S}<br /> {2} < s_n < \frac{{3S}}<br /> {2} \hfill \\ <br /> \end{gathered}
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