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lim_(n→∞) ( ((n+1)(n+2)...3n)/(n²ⁿ))^(1/n) is equal to -

1. 18/e⁴
2. 27/e²
3. 9/e²
4. 3 log 3 - 2

Correct answer: 27/e²

Solution

The limit evaluates the growth rate of the product in the numerator compared to the exponential growth in the denominator. By applying Stirling's approximation and simplifying the expression, we find that the dominant terms lead to the result of 27/e².

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