Geometric Progression
Mediummathematics
The sum of the infinite GP 1/2, 1/4, 1/8, ... is
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Solution
Incorrect! Answer:
1
- Identify Terms: a=1/2. The common ratio r=1/21/4=1/2.
- Convergence Condition: Since ∣r∣<1, the sum to infinity exists.
- Sum Formula: S∞=1−ra.
- Substitution:
- S∞=1−1/21/2=1/21/2.
- Result: 1.
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About This Question
- Subject
- mathematics
- Chapter
- sequence and series
- Topic
- geometric progression
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
1
- Identify Terms: a=1/2. The common ratio r=1/21/4=1/2.
- Convergence Condition: Since ∣r∣<1, the sum to infinity exists.
- Sum Formula: S∞=1−ra.
- Substitution:
- S∞=1−1/21/2=1/21/2.
- Result: 1.
This medium difficulty mathematics question is from the chapter sequence and series, covering the topic of geometric progression. It appeared in the 2025 exam.
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