Evaluate the sum to infinity of the convergent Geometric Progression: 18, 6, 2, 2/3, ...
Answer and explanation
Correct answer: C. 27
- Step 1: Identify first term a = 18 and common ratio r = 6 / 18 = 1/3. Step 2. Check convergence: |r| = 1/3 < 1. Step 3. Sum to infinity formula: S_inf = a / (1 - r) = 18 / (1 - 1/3) = 18 / (2/3) = 18 × (3/2) = 27. Answer: 27. Why not the others: 36 assumes r = 1/2; 24 uses 18 / (3/4); 30 is an estimate.
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