Sequences and Series
In this section we will be taking a look at sequences and infinite series. In fact, this section will deal approximately exclusively with series. Though, we as well need to understand some of the basics of sequences to properly deal with series. Hence, we will spend a some time on sequences also. Series is one of those topics which several students don't find all that helpful. To be honest, several students will never see series outside of their calculus class. Though, series do play an significant role in the field of ordinary differential equations and with no series large portions of the field of partial differential equations would not be probable.
Alternatively, series is an significant topic even if you won't ever see any of the applications. Several applications are beyond the scope of most Calculus courses and tend to take place in classes that several students don't take. Thus, as you go by this material remember that these do have applications even if we won't really be covering so many of them in this class.
Here is a list of terminology in this section.
1. Sequences
2. More on Sequences
3. Series
4. Series - Convergence/Divergence
5. Series - Special Series
6. Integral Test - by Using the Integral Test to find out if a series converges or diverges.
7. Comparison Test/Limit Comparison Test - by Using the Comparison Test and Limit Comparison
8. Tests to ascertain if a series converges or diverges.
9. Alternating Series Test - by Using the Alternating Series Test to ascertain if a series converges or diverges.
10. Absolute Convergence - it provides a brief discussion on absolute convergence and how it differs from convergence.
11. Ratio Test - by Using the Ratio Test to find out if a series converges or diverges.
12. Root Test - by Using the Root Test to find out if a series converges or diverges.
13. Strategy for Series - A set of common guidelines to use when deciding that test to use.
14. Estimating the Value of a Series
15. Power Series
16. Power Series and Functions
17. Taylor Series
18. Binomial Series