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What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
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Practice Questions
1 question
Q1
What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
1.5
2
1
3
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S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
Solution:
S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Steps: 7
Show Steps
Step 1: Identify the series. The series is 1, 1/2, 1/4, 1/8, 1/16.
Step 2: Write down the first 5 terms of the series: 1, 1/2, 1/4, 1/8, 1/16.
Step 3: Add the first term (1) to the second term (1/2). This gives you 1 + 1/2 = 1.5.
Step 4: Add the result (1.5) to the third term (1/4). This gives you 1.5 + 1/4 = 1.5 + 0.25 = 1.75.
Step 5: Add the result (1.75) to the fourth term (1/8). This gives you 1.75 + 1/8 = 1.75 + 0.125 = 1.875.
Step 6: Add the result (1.875) to the fifth term (1/16). This gives you 1.875 + 1/16 = 1.875 + 0.0625 = 1.9375.
Step 7: The sum of the first 5 terms is 1.9375.
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