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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.1 The Geometric Series, #44 · Calculus · Series

How many terms of the series … are needed before the first…

How many terms of the series $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots$ are
needed before the first decimal place doesn't change? Which
power of $\frac{1}{4}$ equals the $100$ th power of $\frac{1}{2}$ ? Which power $1/ a^{n}$ equals
$1/ 2^{100}$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.1 The Geometric Series, #44

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