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where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (mod 6). Equivalently, n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function f defined in the Statement of the problem section of ...
The sticks measure 4 + 3 ⁄ 4 by 1 + 1 ⁄ 4 by 1 + 1 ⁄ 4 inches (121 mm × 32 mm × 32 mm) and are typically sold stacked two by two in elongated cube-shaped boxes. [ 62 ] West of the Rocky Mountains, butter printers standardized on a different shape that is now referred to as the Western-pack shape.
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.
The cup is a cooking measure of volume, commonly associated with cooking and serving sizes.In the US, it is traditionally equal to one-half US pint (236.6 ml). Because actual drinking cups may differ greatly from the size of this unit, standard measuring cups may be used, with a metric cup commonly being rounded up to 240 millilitres (legal cup), but 250 ml is also used depending on the ...
Compound butters (French: beurre composé, pl. beurres composés) are mixtures of butter and other ingredients used as a flavoring, in a fashion similar to a sauce. [1] [2] [3] Compound butters can be made or bought. A compound butter can be made by whipping additional elements, such as herbs, spices or aromatic liquids, into butter.
In German cuisine, Butterbrot (literally: butter bread = bread with butter) is a slice of bread topped with butter.Also known as boterham in Dutch speaking countries, it is still considered Butterbrot or boterham even if additional toppings, such as cheese, spreads, or lunch meats, are added, as long as it begins with a slice of bread with butter.
Sugar pie (tarte au sucre): which possibly came with the arrival of the "King's Daughters" in Quebec during the 1600s, where the imported brides used maple syrup, butter and dried fruit to make a possible precursor to modern examples of the butter tart. [2] The butter tart is sometimes described as a smaller, tart-sized version of the sugar pie.