Image:Sylvester-square.svg

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[edit] Summary

Graphical demonstration of the sum of the reciprocals of Sylvester's sequence,

$1 = \frac12 + \frac13 + \frac17 + \frac1{43} + \frac1{1807} + \cdots$

The first row of 2 squares has side length 1/2, for total area 1/2, the second row of 3 squares has side length 1/3, for total area 1/3, etc. All the squares together fill out the area of a unit square, showing that the total area is 1. Only the first four rows are shown; the bottom row is at distance 1/1806 from the bottom side of the unit square, a distance too small to easily be seen in the figure.

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(del) (cur) 01:23, 5 December 2006 . . David Eppstein (Talk | contribs) . . 256×256 (3,909 bytes) (Graphical demonstration of the sum of the reciprocals of Sylvester's sequence, :<math>1 = \frac12 + \frac13 + \frac17 + \frac1{43} + \frac1{1807} + \cdots</math> The first row of 2 squares has side length 1/2, for total area 1/2, the second row of 3 s)