Alternating series
A series in which the terms are alternately positive and negative is an alternating series. For example, here is the alternating harmonic series:
The Alternating Series Test: The series
converges if all three of the following conditions are satisfied:
- The 's are all positive.
- The positive 's are (eventually) nonincreasing: for all , for some integer .
- .
Developed for use with Thomas' Calculus, published by Pearson.