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The value of 6 + log_(3/2)( (1 / (3*sqrt(2))) * sqrt(4 - (1 / (3*sqrt(2))) * sqrt(4 - (1 / (3*sqrt(2))) * sqrt(4 -... (to infinity))))) is
- 2
- 4
- 6
- 8
Correct answer: 4
Solution
Setting A equal to the infinite nested expression and solving the resulting quadratic gives A = 4/9. Then log_(3/2)(4/9) = log_(3/2)((2/3)²) = 2 * log_(3/2)(2/3) = 2 * (-1) = -2. So the answer is 6 + (-2) = 4.
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