I need to solve this problem
By piling dominoes of 5 cm length, on the others at the edge of a table, we try to realize the biggest possible overhang. Dominoes like in balance under their own weight. For example with 1 domino we realize a 2.5 cm overhang. With 2 dominoes, we can realize a 3.75 cm overhang. How much dominoes is it necessary to realize an overhang of 1 m?
Is it a simple way to solve this equation without using a computer?
$$2.5\left(\sum_{k=1}^n \frac{1}{k}\right)=100\Leftrightarrow H_n=40$$
Thank you in advance