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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.3 Convergence Tests: All Series, #25 · Calculus · Series

If the terms of … are rearranged into …, show that this…

If the terms of $ln 2 = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots$ are rearranged into $1 - \frac{1}{2} - \frac{1}{4} + \frac{1}{3} - \frac{1}{6} - \frac{1}{8} + \dots$ , show that this series now adds to $\frac{1}{2} ln 2$ . (Combine each positive term with the following negative term.)

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.3 Convergence Tests: All Series, #25

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