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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

ParaH2
  • 1,672
  • Not exactly. But this link furnishes a good approximation for the sum, which is a good starting place. – MPW Jul 16 '15 at 01:51
  • You probably do not realise it but there is a slight ambiguity in the question. From what you post you seem to be assuming that your dominoes are in a stack with only one domino on each level. But the way the question is worded that is not a requirement. For the more general case see this paper. – Conrad Turner Jul 16 '15 at 03:28
  • I will read this paper, because the answer i find is false with my method. Thank you – ParaH2 Jul 16 '15 at 12:00

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