If p(n): 2n < (1 2 3 ... n). Then the smallest positive integer f… - Vidyadip

MCQ

If $p(n): 2n < (1 \times 2 \times 3 \times ... \times n).$ Then the smallest positive integer for which $p(n)$ is true is:

A
$1$
B
$2$
C
$3$
✓
$4$

✓

Answer

Correct option: D.

$4$

The smallest positive integer for which $P(n)$ is $4.$
$P(4) = 2^4 < (1 \times 2 \times 3 \times ... \times 4)$
$P(4) = 16 < 24.$

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