Copyright

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.


Learn more about this topic:

Loading...
Power Series: Formula & Examples

from Precalculus: Help and Review

Chapter 2 / Lesson 10
19K

Related to this Question

Explore our homework questions and answers library