Final Thoughts on Infinite Series

After reading this lesson and completing a sufficient number of related exercises, you should be familiar with these concepts:

• the definition of an infinite series
• the definition of convergence of an infinite series
• a test for determining if a given infinite series converges based on its partial sums
• the definition of the geometric series
• a formula for the sum of a convergent geometric series

Although the method that we introduced in this lesson for testing whether a given series converges is important, it is limited. Our method depends on us being able to find an expression for a partial sum, which is often not possible. As such, further lessons in this course explore other strategies that answer our two key questions: given an infinite series, does the series converge, and if it does, what does it converge to?