Editing Harmonic series (mathematics) (section)

===Stacking blocks===
{{main|Block-stacking problem}}
[[File:Block_stacking_problem.svg|thumb|250px|The [[block-stacking problem]]: blocks aligned according to the harmonic series can overhang the edge of a table by the harmonic numbers]]
In the [[block-stacking problem]], one must place a pile of <math>n</math> identical rectangular blocks, one per layer, so that they hang as far as possible over the edge of a table without falling. The top block can be placed with <math>\tfrac12</math> of its length extending beyond the next lower block. If it is placed in this way, the next block down needs to be placed with at most <math>\tfrac12\cdot\tfrac12</math> of its length extending beyond the next lower block, so that the [[center of mass]] of the top two blocks is supported and they do not topple. The third block needs to be placed with at most <math>\tfrac12\cdot\tfrac13</math> of its length extending beyond the next lower block, so that the center of mass of the top three blocks is supported and they do not topple, and so on. In this way, it is possible to place the <math>n</math> blocks in such a way that they extend <math>\tfrac12 H_n</math> lengths beyond the table, where <math>H_n</math> is the {{nowrap|<math>n</math>th}} harmonic number.{{r|graham|sharp}} The divergence of the harmonic series implies that there is no limit on how far beyond the table the block stack can extend.{{r|sharp}} For stacks with one block per layer, no better solution is possible, but significantly more overhang can be achieved using stacks with more than one block per layer.{{r|overhang}}