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Compute the infinite product: 32 * 32^(1/6) * 32^(1/36) *... (terms continue indefinitely). What is the value of this product?

1. 16
2. 32
3. 64
4. 128

Correct answer: 64

Solution

Each factor is 32^(1/6^(n-1)), so the product equals 32 raised to the power (sum of the geometric series 1 + 1/6 + 1/36 +...). The series sums to 1/(1-1/6) = 6/5, giving 32^(6/5) = (2⁵)^(6/5) = 2⁶ = 64.

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