Here are some notes I made last semester for WeBWorK: Series — Taylor and Maclaurin series — #10

This is a straightforward example, but it is somewhat long and requires the use of certain keys that make this approach work.

Remember that there is a second approach to finding the series representation of a function that does not require these keys: given a function and a center, you can always start taking derivatives to find the Taylor series. If you need to answer questions about that Taylor series, you will need to find a pattern for the Taylor coefficients, which is easy in some cases and not so easy in others.