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Question
Let P(n): “2n < (1 × 2 × 3 × ... × n)”. Then the smallest positive integer for which P(n) is true is ______.
Options
1
2
3
4
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Solution
Let P(n): “2n < (1 × 2 × 3 × ... × n)”. Then the smallest positive integer for which P(n) is true is 4.
Explanation:
P(1): 2 < 1 is false.
P(2): 22 < 1 × 2 is false.
P(3): 23 < 1 × 2 × 3 is false.
But P(4): 24 < 1 × 2 × 3 × 4 is true.
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