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Math Help - Series - limits of two series

  1. #1
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    Series - limits of two sequences

    I have a question in the course infinitesimal calculus:

    a_n , b_n are two positive series,
    lim((a_n)/(b_n))=L<infinity

    Prove or give a negative example: if lim(b_n)=0, then lim(a_n)=0.

    It looks very tricky, though I just couldn't find a negative example, or a way to prove it.

    Can you please help me with this?
    Last edited by adam63; November 28th 2009 at 03:37 AM.
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  2. #2
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    I am not the best at these things, but is that not similar to the limit comparison test? Would the proof of that not help you? just curious
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  3. #3
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    Quote Originally Posted by adam63 View Post
    I have a question in the course infinitesimal calculus:

    a_n , b_n are two positive series,
    lim((a_n)/(b_n))=L<infinity

    Prove or give a negative example: if lim(b_n)=0, then lim(a_n)=0.

    It looks very tricky, though I just couldn't find a negative example, or a way to prove it.

    Can you please help me with this?

    It is true: \lim_{n\to\infty}a_n=\lim_{n\to\infty}b_n\cdot \frac{a_n}{b_n} ...now use arithmetic of limits since both sequences converge to a finite limit.

    Tonio
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  4. #4
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    is it 'legal' to presume that a_n has a finite limit, and use arithmetic of limits?
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