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What is the value of the infinite series 1 + (1×3)/6 + (1×3×5)/(6×8) +.......... ?

1. 1
2. 0
3. ∞
4. 4

Correct answer: 4

Solution

Terms t_k = [1.3.5...(2k+1)]/[6.8...(2k+4)] behave like k^(-3/2), so the series converges; summing (numerically and as a hypergeometric value) gives exactly 4.

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