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Find the sum of the infinite series: 1 + 4/7 + 9/49 + 16/343 +...
- 481/271
- 49/27
- 518/344
- 53/34
Correct answer: 49/27
Solution
The general term is n² / 7^(n-1). Using the identity sum n² r^(n-1) = (1+r)/(1-r)³ with r = 1/7 gives (1 + 1/7)/(1 - 1/7)³ = (8/7) / (6/7)³ = (8/7) * (343/216) = 49/27.
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