Unformatted text preview: series is convergent with sum ∞ s n =1 (0 . 8) n1∞ s n =1 (0 . 3) n = 1 1. 83 10 13 10 = 1 1 53 10 7 10 = 53 7 = 32 7 Problem 34 Express the number as a ratio of integers: 6 . 2 54 = 6 . 2545454 · · · This is 6 + 2 10 + 54 1000 + 54 1000 · 1 100 + 54 1000 · p 1 100 P 2 + 54 1000 · p 1 100 P 3 + · · · This consists o± the sum o± two terms plus a geometric series with frst term 54 1000 and multiplier 1 100 . There±ore, the total is = 6 + 1 5 + 54 1000 11 100 = 31 5 + 54 1000 · 100 99 = 31 5 + 54 990 = 31 · 198 + 54 990 = 6192 990 = 344 55...
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This homework help was uploaded on 04/08/2008 for the course MATH 182 taught by Professor Keppelmann during the Spring '08 term at Nevada.
 Spring '08
 Keppelmann
 Geometric Series

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