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Math Help - Proving convergence of {an/bn} given...

  1. #1
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    Proving convergence of {an/bn} given...

    Theorem: If {an} is bounded and {bn} tends to infinity with bn not equal to 0 for all n, then {an/bn} converges to 0.

    I am having trouble understanding why this theorem is true. Can somebody please provide me with a proof?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by gwiz View Post
    Theorem: If {an} is bounded and {bn} tends to infinity with bn not equal to 0 for all n, then {an/bn} converges to 0.

    I am having trouble understanding why this theorem is true. Can somebody please provide me with a proof?
    -\dfrac{K}{|b_n|}\le \left| \dfrac{a_n}{b_b} \right| \le \dfrac{K}{|b_n|}

    where K \ge |a_n| for all $$n \in \mathbb{N}

    CB
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