Question: Prove that if \(\sum a_{n}\) is a conditionally convergent series and \(r\) is any real number, then there is a rearrangement of \(\sum a_{n}\) whose sum is \(r\). [Hints: Use the notation of Exercise 39. Take just enough positive terms \(a_{n}^{+}\) so that their sum is greater than \(r\). Then add just enough negative terms \(a_{n}^{-}\) so that the cumulative sum is less than \(r\). Continue in this manner and use Theorem 12.2.6.]

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