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Math Help - limit proof

  1. #1
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    limit proof

    Let (x sub n) and (y sub n) be sequences of positive numbers such that
    lim(x sub n/y sub n) = 0. Prove if lim(x sub n)= positive infinity, then
    lim(y sub n) = positive infinity.
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  2. #2
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    Quote Originally Posted by hayter221 View Post
    Let (x sub n) and (y sub n) be sequences of positive numbers such that
    lim(x sub n/y sub n) = 0. Prove if lim(x sub n)= positive infinity, then
    lim(y sub n) = positive infinity.
    the conditions on the terms of the sequences and:

    \lim(x_n/y_n) = 0

    means that for all positive \varepsilon eventually

    0 < x_n/y_n<\varepsilon

    so:

    x_n<\varepsilon y_n

    and as x_n goes to \infty so must y_n.

    Now make this argument more formal and fill in the detail

    CB
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