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Math Help - Question on series

  1. #1
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    Question on series

    Given that x_i - y_i goes to zero as i goes to infinity and that the ∑ x_i converges, show that ∑ y_i may diverge.

    I don't understand this question. Am I supposed to prove this using ∑ y_i as some arbitrary sequence, or can I come up with some example with real numbers?
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  2. #2
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    Krizalid's Avatar
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    let x_i=\frac1{i^2}, y_i=\frac1i, clearly the difference goes to zero, but \sum y_i diverges.
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  3. #3
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    You have simply to put a concrete example such that this situation happens. take y_i=\frac{1}{i}, and x_i any convergente sequence.
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