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If xₙ = cos(pi/2ⁿ) + i sin(pi/2ⁿ), find the value of the infinite product x₁ * x₂ * x₃ *... (to infinity).

1. -1
2. 1
3. 0
4. infinity

Correct answer: -1

Solution

The product equals e^(i*pi*(1/2+1/4+...)) = e^(i*pi) = -1.

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