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Thread: Convergence/Divergence Proof

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    Convergence/Divergence Proof

    Prove or provide a counterexample: If $\displaystyle (s_n)$ and $\displaystyle (\frac {s_n}{t_n})$ are convergent sequences and $\displaystyle $t_n \neq 0$$ for all $\displaystyle $n$$, then $\displaystyle $t_n$$ converges.
    Last edited by topsquark; Nov 6th 2017 at 09:20 AM.
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  2. #2
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    Re: Convergence/Divergence Proof

    Quote Originally Posted by mmstone14 View Post
    Prove or provide a counterexample: If $\displaystyle (s_n)$ and $\displaystyle (\frac {s_n}{t_n})$ are convergent sequences and $\displaystyle $t_n \neq 0$$ for all $\displaystyle $n$$, then $\displaystyle $t_n$$ converges.
    What if $s_n=\dfrac{1}{n}~\&~t_n=n~?$
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