Question 2
Prove that there exists a finite sequence of distinct positive integers $n_1, n_2, \dots, n_k$, such that
$$
2012 \lt \sum_{i=1}^{k} \frac{1}{n_i} \lt 2012 + \left(\frac{1}{2012}\right)^{2012}.
$$
$$
2012 \lt \sum_{i=1}^{k} \frac{1}{n_i} \lt 2012 + \left(\frac{1}{2012}\right)^{2012}.
$$