Sec. 8.2 HW

Sec. 8.2 HW - series is convergent with sum ∞ s n =1(0 8...

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Math Homework 8.2 Problem 12 Determine if the geometric series is convergent. If it is convergent, then Fnd its sum: 1 + 0 . 4 + 0 . 16 + 0 . 064 + . . . Notice that this geometric series has frst term a = 1 and multiplier r = 0 . 4 since 0 . 4 = 0 . 4 1 = 0 . 16 0 . 4 = 0 . 064 0 . 16 Because | 0 . 4 | < 1 this series converges with total sum 1 + 0 . 4 + 0 . 16 + 0 . 064 + . . . = 1 1 - 0 . 4 = 1 0 . 6 = 1 6 10 = 1 3 5 = 5 3 Problem 24 Determine whether the series is divergent or convergent. If it is convergent, then Fnd its sum: s n =1 b (0 . 8) n - 1 - (0 . 3) n B Notice this is the diFerence o± two series: s n =1 (0 . 8) n - 1 - s n =1 (0 . 3) n The frst series has initial term 1 and multiplier 0.8 whereas the second series has frst term 0 . 3 and multiplier 0 . 3. Since both o± these multipliers ±all in the range needed ±or convergence the total
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Unformatted text preview: series is convergent with sum ∞ s n =1 (0 . 8) n-1-∞ s n =1 (0 . 3) n = 1 1-. 8-3 10 1-3 10 = 1 1 5-3 10 7 10 = 5-3 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 1-1 100 = 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.

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