Question

Question:In Problem find the first three nonzero terms in the power series expansion for the product f(x)g(x).

Short answer

The first three nonzero terms of the product of the given power series are

Step-by-step solution

Given non- zero terms for given power series

For two power series and with nonzero radii ofconvergence, the product is also a power series given by

where the coefficient is

Find non- zero terms for given power series

To find the first three nonzero terms of the product, find the first three nonzero coefficients.

In this case,

For n =0 , we have:

Therefore,is a first nonzero coefficient

For n=1, we have:

Therefore,is a second nonzero coefficient

For n=1, we have:

Therefore, the first three nonzero terms of the product of the given power series are