a. Consider the number 0.555555 . . ., which can be viewed as the series Evaluate the

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a. Consider the number 0.555555 . . ., which can be viewed as the series -k 5Σ10. k=1 Evaluate the geometric series to obtain a rational value of 0.555555 . .

b. Consider the number 0.54545454 . . ., which can be represented by the series 54 10-24. k=1 Evaluate the geometric series to obtain a rational value of the number. 

c. Now generalize parts (a) and (b). Suppose you are given a number with a decimal expansion that repeats in cycles of length p, say, n1, n2 . . . , np, where n1, . . . ,np are integers between 0 and 9. Explain how to use geometric series to
obtain a rational form for

d. Try the method of part (c) on the number

e. Prove that

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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