Question

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

• A. 4
• B. 2
• C. 5
• D. 3

Answer 1

Answer: (A)

$P\left(n\right);2^n<n!$
$n=2;2^2=4,n!=2!=2$
$4\nless 2$
$n=3;2^3=8,3!=6$
$8\nless 6$
$n=4;2^4=16,4!=24$
$16<24$
$\therefore n=4$