$factorial(n)\; \ge \; 2nwhen\; n\; \ge \; 4$

since it uses induction and I am out of practise.#### Base case

For n = 4factorial(4) = 4*3*2*1 = 24

and 2^{4} = 2*2*2*2 = 16

and 24 ≥ 16

so $factorial(n)\; \ge \; 2nwhen\; n\; =\; 4$

#### Induction step

For n >= 4 assume we have$factorial(n)\; >=\; 2n$

and consider
$factorial(n+1)\; =\; factorial(n)\; \times \; (n+1)$

≥ 2^{n} × (n+1)

≥ 2^{n} × 2 since (n+1) ≥ 2 when n ≥ 4

= 2^{n+1}

(I also wanted to learn about writing maths in html)