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The idea becomes clearer by considering the general series 1 − 2 x + 3 x2 − 4 x3 + 5 x4 − 6 x5 + &c. that arises while expanding the expression 1⁄(1+x)2, which this series is indeed equal to after we set x = 1.
In order to transform the series 1 + 2 + 3 + 4 + ⋯ into 1 − 2 + 3 − 4 + ⋯, one can subtract 4 from the second term, 8 from the fourth term, 12 from the sixth term, and so on.
Current ISO 3166 country codes. The sortable table below contains the three sets of ISO 3166-1 country codes for each of its 249 countries, links to the ISO 3166-2 country subdivision codes, and the Internet country code top-level domains (ccTLD) which are based on the ISO 3166-1 alpha-2 standard with the few exceptions noted.
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ISO 3166-1 alpha-2 – two-letter country codes which are the most widely used of the three, [citation needed] and used most prominently for the Internet's country code top-level domains (with a few exceptions). ISO 3166-1 alpha-3 – three-letter country codes which allow a better visual association between the codes and the country names than the alpha-2 codes. ISO 3166-1 numeric – three ...
The series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ lends itself to some particularly simple visual demonstrations because a square and a triangle both divide into four similar pieces, each of which contains 1 4 the area of the original.
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