Prove by induction that for any $n \ge 2$ : $\sum_{k=n+1}^{2n}\frac{1}{k} \ge \frac{13}{24}$
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction