Question 63
Prove the inequality
$$
\frac{1}{k} + \frac{1}{k+1} + \dots + \frac{1}{n} \ge \frac{2(n-k+1)}{n+k}
$$
for all pairs $(n, k)$ of positive integers such that $k \le n$.
$$
\frac{1}{k} + \frac{1}{k+1} + \dots + \frac{1}{n} \ge \frac{2(n-k+1)}{n+k}
$$
for all pairs $(n, k)$ of positive integers such that $k \le n$.