# Suppose two Maclaurin series are multiplied together. If first Maclaurin series has a radius of...

## Question:

Suppose two Maclaurin series are multiplied together. If first Maclaurin series has a radius of convergence of one and the second has radius of convergence of {eq}\pi {/eq}, what is the radius of convergence of the product of the two series?

## Power Series:

The sum of convergent power series is always a convergent power series.

We cannot generalize this same result to the product of power series.

## Answer and Explanation:

Taking into account that the convergent series product does not have to generate a convergent series, we cannot obtain a general result in this regard.

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