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### High School Mathematics - 23.6 Sum of Geometric Series

 Geometric series is the sum of geometric sequence. Example: a) 1 + 2 + 4 + 8 + 16 + ......... + 1024 b) 2 + 6 + 18 + 54 +........... + 118098 Method 1: 1) Write the sum in an ordinary order 2) Write the sum again by multiplying by the ratio 3) Subtract both the sums. 4) Solve for S Question: Find the sum of the series 2 + 6 + 18 + 54 +........... + 486 Then by subtracting 3S - S all the terms except the first and last cancel out: S = 2 + 6 + 18 + 54 +........... + 486 3S = 6 + 18 + 54 +........... + 486 + (486x3) ----------------------------------------------------------- 3S-S = 486 x 3 - 2 2S = 486 x 3 - 2 2S = (1458 - 2) 2S = 1456 S = 728 Answer: The sum of the series is 728 Directions: Find the sum of the geometric series below. Also write at least 5 examples of your own.
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