4PM1/02 Jun 2023, Question 2: Geometric Progressions and Sum to Infinity
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks
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The question, in short
A convergent geometric series has nth term 8^(1 − 2n). Find its sum to infinity and express the result as p/q with integers p and q.
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Solution · 6 marks
- 1n = 1: a = 8^(−1) = 1/8
- 2n = 2: ar = 8^(−3), so r = 8^(−3)/8^(−1) = 8^(−2) = 1/64
- 3S∞ = a/(1 − r) = (1/8)/(1 − 1/64)
- 4= (1/8) × (64/63) = 8/63
Answer8/63
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