We have already seen, studying the geometric series of ratio 1/4, that a geometric series
is a convergent series when the ratio is less than 1. Its sum is:
A simple case is when the ratio is
Then, the geometric series we want to add can be represented in this way:
The sum of the geometric series of ratio 1/2 is:
In this visualization we have used a rectangle with a particular shape: when we cut it in half we get two rectangles with the same shape. This aspect ratio is used, for example, in the international papel size standard, ISO 216 (based on the German DIN, for example, DIN A4).
The aspect ratio of these rectangles is:
In the animation, these rectangles follow a kind of spiral around a point. ¿Can you think what are its coordinates? The result is related with another geometric series: the geometric series of ratio 1/4.
LINKS
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Sum of a geometric series of ratio 1/4
One intuitive example of how to sum a geometric series. A geometric series of ratio less than 1 is convergent.
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Standar Paper Size DIN A
There is a standarization of the size of the paper that is called DIN A. Successive paper sizes in the series A1, A2, A3, A4, and so forth, are defined by halving the preceding paper size along the larger dimension.
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Geometric sequence
Geometric sequences graphic representations
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