Question

$2^n>n^2$ when $n\in N$ such that

• A. $n>2$
• B. $n>3$
• C. $n<5$
• D. $n\ge 5$

Answer 1

Answer: (D)

Let the given statement be $P(n)$, then
$P(1)\Rightarrow 2^1>1^2$ which is true
$P(2)\Rightarrow 2^2>2^2$ which is false
$P(3)\Rightarrow 2^3>3^2$ which is false
$P(4)\Rightarrow 2^4>4^2$ which is false
$P(5)\Rightarrow 2^5>5^2$ which is true
$P(6)\Rightarrow 2^6>6^2$ which is true
$\therefore P(n)$ is true when $n\ge 5$