Sometimes we’ll be asked for the radius and interval of convergence of a Taylor series. In order to find these things, we’ll first have to find a power series representation for the Taylor series.

Read MoreThe comparison test for convergence lets us determine the convergence or divergence of the given series by *comparing* it to a similar, but simpler comparison series. We’re usually trying to find a comparison series that’s a geometric or p-series, since it’s very easy to determine the convergence of a geometric or p-series.

The alternating series estimation theorem gives us a way to approximate the sum of an alternating series with a remainder or error that we can calculate. To use the theorem, the alternating series must follow two rules.

Read MoreSometimes it’s easy to forget that there’s a difference between the *limit* of an infinite series and the *sum* of an infinite series. They’re two very different things, and we use a different calculation to find each one.

One convenient way to find the sum of the Maclaurin series is to start with a well-known Maclaurin series and then manipulate it one step at a time until it matches the series you’ve been given. Because you’ll be manipulating the expression of the sum at the same time, once you get the series to match, you’ll automatically have the sum.

Read MoreIf you need to find the sum of a series, but you don’t have a formula that you can use to do it, you can instead add the first several terms, and then use the integral test to estimate the very small remainder made up by the rest of the infinite series. The sum of the series is usually the sum of the first several terms, plus a very smaller error that you can estimate.

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