Use the binomial series to expand the function as a power series. Find the radius of convergence. x/ â 9+ x^2

Step-by-step explanation:

The given function is:

Using the binomial series:

To compute the radius of convergence:

Suppose

Then, rewriting the equation above as:

As such;

However, the series converges if and only if:

∴

explanation:

remove parenthesis:

=

apply rule

=

multiply fractions:

=

=

divide:

=

mordancy.