How to prove the following inequality by mathematical induction?
$$x + \frac 1x \ge 2, x \gt 0$$
I am aware of this.
First, I have to prove $P(1)$; then $P(n+1)$.
I am stuck at $P(n+1)$ because I do not know how to add the plus one to it. thanks.
I misunderstood the problem; I thought I needed to prove the above inequality by mathematical induction; I learnt that I just need to prove it. I think the easiest way to prove this inequality is by constructing a direct proof.