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

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 = 59 048

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 3n – 1 = 243 S6 = log33n – 1 = log3243 = 728 n - 1 = log3243 ln 243 ln 3 n - 1 = n – 1 = 5 n = 6

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