I'm struggling around my homework. I hope someone will point me the right direction for solving following examples:
Prove that $n^{n+1} > (n + 1)^n$ for $n > 2$;
Prove that $(1 + x)^n \ge 1 + nx$; $x \in\Bbb R$; $n \in\Bbb N$;
Prove that $(2n)! < 2^{2n}(n!)^2$; $n \ge 1$;
Prove that $2^n > n$:
Thank you a lot.