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Thread: Series convergence, division

  1. #1
    Sep 2010

    Series convergence, division

    Hello, I have bumped into this forum a few times in the past and now come here hoping to get some help. Over the past two weeks of my math subject, I got really behind to the point of not even being able to understand the suggested practice questions..

    "Suppose there are sequences a0, a1, a2... and b0, b1, b2... of integers.
    Prove that the functions A(x) = a0 + a1x + a2x^2+... and B(x) = b0 + b1x + b2x^2..
    converge whenever the following holds:

    This looks very much related to the ratio test, but what am I to do with the * x part? I don't understand where the x comes from in there.

    Secondly, "What are a necessary and sufficient set of conditions on these integer sequences in order to satisfy A(x) * B(x) = 1 for all real x such that A(x), B(x) are defined"
    Completely stumped with the constraint of the sequences being integer. How would you define these sequences - recurrence relation?

    I hope this is the correct section, its a bit iffy.
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  2. #2
    MHF Contributor
    Oct 2009
    This looks very much related to the ratio test
    This is exactly the ratio test.

    The question about the product A(x) * B(x) has been discussed in this thread:
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