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KCET2020MathematicsSequences and Series

If P(n): 2^ n < n ! Then the smallest positive integer for which P(n) is true if

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

C. 4

Step-by-step solution

We have, aligned &P(n)=2^ n < n ! &P(1)=2 < 1 ! False aligned aligned &P(2)=2² < 2 ! False &P(3)=2³ < 3 ! False &P(4)=2⁴ < 4 ! True aligned The smallest position integer for which P(n) is true for n=4 .

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