Question 52
For any positive integer $k$ define
$$
H_k = 1 + \frac{1}{2} + \dots + \frac{1}{k}.
$$
Prove the relation
$$
1 + \frac{1}{n+1} \sum_{k=1}^{n} H_k = H_{n+1}.
$$
$$
H_k = 1 + \frac{1}{2} + \dots + \frac{1}{k}.
$$
Prove the relation
$$
1 + \frac{1}{n+1} \sum_{k=1}^{n} H_k = H_{n+1}.
$$