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11.4 – Infinite Geometric Series

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Sum of an Infinite Geometric Series

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The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible.

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + …

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r =

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ ½

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾ ½

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r = ½ 1 – ¾

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r = ½ = ½ 1 – ¾ ¼

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Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r = ½ = ½ = 2 1 – ¾ ¼

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b) 1 – 2 + 4 – 8 + …

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r =

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b) 1 – 2 + 4 – 8 + … r = -2 1

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible.

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 1 – r

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 = 20 1 – r 1 – (- ¼)

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 = 20 = 20 1 – r 1 – (- ¼) 5 / 4

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b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 = 20 = 20 = 16 1 – r 1 – (- ¼) 5 / 4

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Ex. 3 Write the following repeating decimals as fractions.

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__ a) 0.39

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Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 99

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Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33

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Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33 ___ b) 0.246

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Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33 ___ b) 0.246 = 246 999

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Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33 ___ b) 0.246 = 246 = 82 999 333

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