Question

5) Suppose -1 an is a conditionally convergent series and let L E IR be arbitrary. Give an informal justification for each of the following. a. We can add up positive terms first, until the first time the sum is greater than L. Then we can add negative terms until the first time the resulting sum is less than L again. Moreover, we can always repeat this process. In repeating the process described in part a, at some point, each time we go past L in either direction, the difference between the current sum and L will get progressively smaller b. c. By adding up the terms of this series in this way (i.e. by rearranging them) we can make the resulting rearranged series converge to L. NOTE: This justifies what we said in class last night. Namely, that for conditionally convergent series, the order in which we add things up MATTERS!

Answer 1

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