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For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...
Buy one, get one free. " Buy one, get one free " or " two for the price of one " is a common form of sales promotion. Economist Alex Tabarrok has argued that the success of this promotion lies in the fact that consumers value the first unit significantly more than the second one. So compared to a seemingly equivalent "Half price off" promotion ...
Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n; this coefficient can be computed by the multiplicative formula. which using factorial notation can be compactly expressed as.
ASCII ( / ˈæskiː / ⓘ ASS-kee ), [ 3]: 6 an acronym for American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices.
Arizona is the sixth largest state by area, ranked after New Mexico and before Nevada. Of the state's 113,998 square miles (295,000 km 2 ), approximately 15% is privately owned. The remaining area is public forest and parkland, state trust land and Native American reservations.
Ohio ( / oʊˈhaɪ.oʊ / ⓘ oh-HY-oh) [ 14] is a state in the Midwestern region of the United States. Ohio borders Lake Erie to the north, Pennsylvania to the east, West Virginia to the southeast, Kentucky to the southwest, Indiana to the west, and Michigan to the northwest. Of the 50 U.S. states, it is the 34th-largest by area.
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