If P (n ) :2^n

Question

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

Accepted Answer

Correct answer: B. (b) : Here P (n ) :2^n<n ! If n=2, then 2^2=4 and 2 !=2, so 4 ≮2. If n=3, then 2^3=8 and 3 !=6, so 8 ≮6 If n=4, then 2^4=16 and 4 !=24, so 16<24 ∴ The smallest positive integer for which P (n ) is true is 4 .

$If P (n) : 2^{n} < n! then the smallest positive integer for which P (n) is true, is$

Solution

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