# Infinite series

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

Note:

1. Sum replaces the symbol for summation

2. an and bn are nth elements of the two series

https://brainmass.com/math/calculus-and-analysis/infinite-series-convergence-3823

#### 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.

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