Question 45
Verify the correctness of the equality:
$$
\sum_{k=1}^{n} \frac{(-1)^{k+1}}{k} \binom{n}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}.
$$
$$
\sum_{k=1}^{n} \frac{(-1)^{k+1}}{k} \binom{n}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}.
$$