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    Show that multiplication of an absolutely convergent series and bounded series is convergent.

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    Suppose the series ak (the k is subscript) converges absolutely and that the series bk is bounded.

    Show that the series ak*bk converges absolutely.

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    https://brainmass.com/math/basic-algebra/show-that-multiplication-of-an-absolutely-convergent-series-and-bounded-series-is-convergent-6693

    Solution Preview

    Since bk is bounded, we know that there exists some bound M such that

    |bk| < M for all k
    ( |bk| is "modulus of bk")

    We also know that sum(|ak|)=N, (where N, of course, is ...

    Solution Summary

    Multiplication of an absolutely convergent series and bounded series is shown to be convergent.

    $2.49

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