Use the Cauchy-Schwarz Inequality to show that for any positive integer n, $\frac{2n}{n+1} \leq 1 + \frac{1}{2} + \cdots + \frac{1}{n}$
I'm having some trouble understanding how the Cauchy Schwarz Inequality can be applied to this. I've tried separating the $\frac{2n}{n+1}$ into two parts, but I'm getting nowhere with that.