Question Detail
Question
If P(n): 3ⁿ > 2ⁿ for all n ≥ 1, what is the smallest n for which this holds?
Correct Answer
Option B is the correct answer.
Detailed Explanation
For n=1: 3¹ = 3, 2¹ = 2, so 3 > 2, true. For n=0: 3⁰ = 1, 2⁰ = 1, so 1 > 1 is false. Therefore the smallest n for which the inequality holds is n=1.
Hint
Test small values of n starting from 1.