Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D

4

(d) 4

Since,

P(1) : $2<1$ is false

P(2) : $2^2<1\times 2$ is false

P(3) : $2^3<1\times 2\times 3$ is false

But P(4) : $2^4<1\times 2\times 3\times 4$ is true.