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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 Preview

    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 ...

    Solution Summary

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