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Date:___________________

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High School Mathematics - 2
3.6 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.

Name: ___________________

Date:___________________

High School Mathematics - 2
3.6 Sum of Geometric Series

Q 1: Find the sum of the geometric series: 4 + 8 + 16 + 32 + 64 + . . . . . . . 2048
3800
5002
4092

Q 2: Find the sum of the geometric series: 1 + 3 + 9 +......729
2199
1093
1090

Q 3: Find the sum of the geometric series: 5 + 25 + 125 + ........ + 3125
2009
3095
4000

Q 4: Find the sum of geometric series: 3 + 6 + 12 + 24 + .........1536
4098
3069
2686

Q 5: Find the sum of the geometric series: 1/2 + (-1) + 2 + (-4) + 8 + (-16) + 32
23/25
43/2
17/19

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........)
45 17/18
47 63/64
38 19/20

Q 7: Find the sum of the geometric series: 1/2 + 3/4 + 7/8 + 15/16 + 31/32 + 63/64
5 1/64
7 1/20
4 2/56

Q 8:
Answer:

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Question 10: This question is available to subscribers only!


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