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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.
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.
The United States is divided into five Petroleum Administration for Defense Districts, or PADDs. These were created during World War II under the Petroleum Administration for War to help organize the allocation of fuels derived from petroleum products, including gasoline and diesel (or "distillate") fuel. Today, these regions are still used for data collection purposes.
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Who’s afraid of buying 30-plus “Tortured Poets Department” album variants? Between her ongoing record-shattering “Eras” tour and the album holding the No. 1 spot on the Billboard 200 ...
This article lists computer monitor, television, digital film, and other graphics display resolutions that are in common use. Most of them use certain preferred numbers .
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.
Explore the Collatz conjecture, a simple mathematical problem that remains unsolved despite many attempts. Learn about its history, variations and applications.