Taylor's inequality lets you find the remainder (also called the error) of your series approximation.

A Taylor series is just the power series representation of a function. You can use the method in this video to find the Taylor series of a function.

The binomial series is a special type of power series.

Sometimes functions are easier to integrate when you integrate the power series representation of the function, rather than the function itself. In this case, replace the function with the first few terms of its power series representation, and then integrate.

The interval of convergence of a series is the full interval over which the series converges, for example 1<x<5, or [1,5]. You can use the ratio test to find the interval of convergence.

The limit of an infinite series is the value the series approaches when you choose larger and larger values for n (this would also be the horizontal asymptote of the series). In contrast, the sum of the infinite series is the value you get when you add together every term in the series.

Use the root test to say whether or not a series is convergent. The root test can be especially useful when the entire series is raised to the same power.

The ratio test can be especially useful for determining the convergence of a series that includes a factorial term, like (n+1)!.

Use the ratio test to say whether or not a series is convergent.

Use the alternating series test to say whether or not an alternating series is convergent. This test can only be applied to alternating series, but it proves that an alternating series is convergent is the series is decreasing and if its limit is 0.