# 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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##### Solution Summary

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

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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 ...

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