MTH 172 Lecture Notes - Lecture 21: Alternating Series Test, Alternating Series, Conditional Convergence
Document Summary
Provide a generalization to each of the key terms listed in this section. Alternating series are types of series that alternate (hence the name) between negative and positive terms. If you have an alternating series such as the following: X n=1 ( 1)n bn = b1 b2 + b3 b4 + b5 bn > 0. There are two scenarios to note that the series is convergent, which are the following: bn bn+1 f or all n. If that is the case, then the following would occur: Rn actually helps denote the given nth remainder or even the error that is between both the nth partial sum and even the in nite series" true value. Any series in the form of p an can be considered absolutely convergent if the given series of the following absolute values is actually convergent: Whenever you have alternating series that is not absolutely convergent, then it is actually consid- ered to be conditionally convergent.
