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What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
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What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
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The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.
Questions & Step-by-step Solutions
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Q
Q: What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
Solution:
The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.
Steps: 8
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Step 1: Identify the first term (a) of the series. In this case, the first term is 1.
Step 2: Identify the common ratio (r) of the series. Here, each term is half of the previous term, so r = 1/2.
Step 3: Use the formula for the sum of an infinite geometric series, which is S = a / (1 - r).
Step 4: Substitute the values of a and r into the formula: S = 1 / (1 - 1/2).
Step 5: Calculate the denominator: 1 - 1/2 = 1/2.
Step 6: Now substitute this back into the formula: S = 1 / (1/2).
Step 7: Dividing by 1/2 is the same as multiplying by 2, so S = 1 * 2 = 2.
Step 8: Therefore, the sum of the infinite geometric series is 2.
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