Question 1
For every positive integer $n$, let
$$
h(n) = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n}
$$
For example, $h(1) = 1$, $h(2) = 1 + \frac{1}{2}$, $h(3) = 1 + \frac{1}{2} + \frac{1}{3}$. Prove that for $n = 2, 3, 4, \ldots$
$$
n + h(1) + h(2) + h(3) + \cdots + h(n-1) = n h(n)
$$
$$
h(n) = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n}
$$
For example, $h(1) = 1$, $h(2) = 1 + \frac{1}{2}$, $h(3) = 1 + \frac{1}{2} + \frac{1}{3}$. Prove that for $n = 2, 3, 4, \ldots$
$$
n + h(1) + h(2) + h(3) + \cdots + h(n-1) = n h(n)
$$