Lecture 8: Convergence Tests for Series; Power Series

In this lecture we will first continue the discussion of the available tests to determine whether or not a series is convergent. After that, we turn to the important notions of limsup and liminf. These new notions are needed to state the general form of the convergence tests. Once we have limsup, we can define the radius of convergence for a power series. Power series are infinite sums of polynomials.