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Infinite series

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If series Sum(an) and Sum(bn) with positive terms are convergent, is the series Sum(an*bn) converegent?

1. Sum replaces the symbol for summation
2. an and bn are nth elements of the two series

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Solution Summary

This shows how to determine if a series based on thes um of two other series is convergent.

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Consider the series Sum(an).
1.We are given that Sum(an) is convergent
2.Claim {an} is a bounded sequence,
i.e. there exists M such that for
all n |an|<=M. (Since all ...

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