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# 5.6 Sum of Geometric Series (1/4)

5.6 Sum of Geometric Series (1/4). a(r n -1) r-1. a(1-r n ) 1-r. S n = for |r|&gt;1. S n = for |r|&lt;1. Term Number. First Term. Common Ratio. Sum (add) to n terms. 5.6 Sum of Geometric Series (2/4). Example: Find the sum of the first 10 terms of 2 + 6 + 18 + ….

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## 5.6 Sum of Geometric Series (1/4)

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1. 5.6 Sum of Geometric Series (1/4) a(rn-1) r-1 a(1-rn) 1-r Sn= for |r|>1 Sn= for |r|<1 Term Number First Term Common Ratio Sum (add) to n terms

2. 5.6 Sum of Geometric Series (2/4) Example: Find the sum of the first 10 terms of 2+6+18+ … a(rn – 1) r - 1 r = 6÷2 = 3 Sn = since |3|>1 a = 2 2x(310 – 1) 3 - 1 S10 = n = 10 = 59048

3. 5.6 Sum of Geometric Series (3/4) Example: Evaluate 2+6+18+ … + 486 Find n Find Sn a(rn – 1) r - 1 r = 6÷2 = 3 Tn = a rn – 1 Sn = since |3|>1 a = 2 486 = 2x3n – 1 2x(36 – 1) 3 - 1 Tn = 486 S6 = 3n – 1 = 243 log33n – 1 = log3243 = 728 n - 1 = log3243 ln 243 ln 3 n - 1 = n – 1 = 5 n = 6

4. 5.6 Sum of Geometric Series (4/4) Example: Evaluate a(rn – 1) r - 1 Sn = since |3|>1 9x(36 – 1) 3 - 1 S6 = a = 9 r = 3 n = 6 = 9837

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