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World Book Encyclopedia. The World Book Encyclopedia is an American encyclopedia. [1] World Book was first published in 1917. Since 1925, a new edition of the encyclopedia has been published annually. [1] Although published online in digital form for a number of years, World Book is currently the only American encyclopedia which also still ...
The World Book Dictionary was last edited and updated by Robert and Cynthia Barnhart in 1996. Robert Barnhart died in 2007, and Cynthia Barnhart went on to produce the Facts on File Student's Dictionary of American English (2008). David Barnhart continues to edit the Barnhart Dictionary Companion and the Barnhart New-Words Concordance. [1]
The only Catalan numbers Cn that are odd are those for which n = 2k − 1; all others are even. The only prime Catalan numbers are C2 = 2 and C3 = 5. [1] The Catalan numbers have the integral representations [2] [3] which immediately yields . This has a simple probabilistic interpretation.
World Book, on the other hand, sells for $1,099 per set. That’s the price listed on their website for the 2024 edition. There’s an interesting claim there, too.
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...
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