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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.3 Convergence Tests: All Series, #40 · Calculus · Series

Every number … between … and 1 equals … with a suitable…

Every number $s$ between $- 1$ and 1 equals $\pm \frac{1}{2} \pm \frac{1}{4} \pm \frac{1}{8} \pm \dots$ with a suitable choice of signs. (Add $1 = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots$ to get Problem 39.) Which signs give $s = - 1$ and $s = 0$ and $s = \frac{1}{3}$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.3 Convergence Tests: All Series, #40

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