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Math Help - Series Convergence

  1. #1
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    Series Convergence

    Hello,
    I have a statement I must prove or disaprove with a counter example, The statement is:
    For each series bn that goes to infinity (bn -> inf), exists a series an that has both of these properties:
    1.The series an converges
    2.The series an*bn diverges.

    My intuition says the statement is true, but Im struggling proving it.

    Thanks a lot,
    Michael.
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  2. #2
    Junior Member nimon's Avatar
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    Re: Series Convergence

    Just off the top of my head, and without being exactly sure what you're asking, could you try a_{n} = \frac{1}{b_{n}^{2}}?
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  3. #3
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    Re: Series Convergence

    bn = ln(x)
    1/bn^2 = 1/ln(x)^2 => Does not converge (The first property required)
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  4. #4
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    Re: Series Convergence

    Quote Originally Posted by MichaelEngstler View Post
    Hello,
    I have a statement I must prove or disaprove with a counter example, The statement is:
    For each series bn that goes to infinity (bn -> inf), exists a series an that has both of these properties:
    1.The series an converges
    2.The series an*bn diverges.

    My intuition says the statement is true, but Im struggling proving it.

    Thanks a lot,
    Michael.
    Are you talking about series or sequences, they are not the same thing!

    .
    Thanks from nimon
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