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One can then prove that this smoothed sum is asymptotic to − + 1 / 12 + CN 2, where C is a constant that depends on f. The constant term of the asymptotic expansion does not depend on f: it is necessarily the same value given by analytic continuation, − + 1 / 12 . [1]
An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [1] The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems ...
The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
[1] Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
[1] [2] The cancellation technique, with part of each term cancelling with part of the next term, is known as the method of differences. An early statement of the formula for the sum or partial sums of a telescoping series can be found in a 1644 work by Evangelista Torricelli, De dimensione parabolae. [3]
Manuel said on ESPN’s rankings show that the committee moved Alabama ahead of Miami in part because the Tide are 3-1 against teams currently ranked in the playoff’s top 25 and Miami is 0-1.
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