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For a natural number n, the inequality 2^(n - 1) < nⁿ holds when

1. n < 2
2. n > 2
3. n ≥ 2
4. it never holds

Correct answer: n ≥ 2

Solution

For n=1, 2^0=1 is not less than 1^1=1, so it fails. For n=2, 2^1=2 < 2^2=4, and it holds for every larger n. Hence 2^(n-1) < n^n holds for n >= 2.

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