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Infinite series

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

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.