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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.
 Q 1: Find the sum of the geometric series: 4 + 8 + 16 + 32 + 64 + . . . . . . . 2048409250023800 Q 2: Find the sum of the geometric series: 1 + 3 + 9 +......729109010932199 Q 3: Find the sum of the geometric series: 5 + 25 + 125 + ........ + 3125309540002009 Q 4: Find the sum of geometric series: 3 + 6 + 12 + 24 + .........1536409830692686 Q 5: Find the sum of the geometric series: 1/2 + (-1) + 2 + (-4) + 8 + (-16) + 3223/2517/1943/2 Q 6: Find the sum of the geometric series: 3 1/5 + 5 1/4 + 7 1/8 + 9 1/16 + 11 1/32 + 13 1/64. (Hint: 3 1/2 can be written as 3 + 1/2, 5 1/4 can be written as 5 + 1/4........)38 19/2047 63/6445 17/18 Q 7: Find the sum of the geometric series: 1/2 + 3/4 + 7/8 + 15/16 + 31/32 + 63/645 1/647 1/204 2/56 Q 8: Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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