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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.1 The Geometric Series, #7 · Calculus · Series

Start with the fraction

Start with the fraction $\frac{1}{7}$ . Divide 7 into $1.000 \dots$ (by long division or calculator) until the numbers start repeating. Which is the first number to repeat? How do you know that the next $____$ digits will be the same as the first?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.1 The Geometric Series, #7

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