Science:Infinite Series Module/Units/Unit 1/1.3 Infinite Series/1.3.10 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?