Three infinite series are given below.
I. n=1∑∞n(−1)n
II. n=1∑∞n21
III. n=1∑∞(−1)nn3/21
Answer the following questions about the nature of each series.
a. Explain the distinction between absolute convergence and conditional convergence for an infinite series. Your explanation should clearly state what property separates the two classifications.
b. For each series I–III, determine whether the series is absolutely convergent, conditionally convergent, or divergent. Justify each conclusion with appropriate reasoning.
c. Select one of the three series and describe how its classification would affect the outcome if its terms were rearranged. Provide a justification based on the classification you determined.