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This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
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 ...
In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
An interpretation of Plato's number is a solution for k = 3. For this special case of m = 1, some of the known solutions satisfying the proposed constraint with n ≤ k, where terms are positive integers, hence giving a partition of a power into like powers, are: [3] k = 3 3 3 + 4 3 + 5 3 = 6 3 k = 4 95800 4 + 217519 4 + 414560 4 = 422481 4 ...
Coverage of this topic in Smithsonian magazine describes the Numberphile video as misleading and notes that the interpretation of the sum as − + 1 / 12 relies on a specialized meaning for the equals sign, from the techniques of analytic continuation, in which equals means is associated with. [35]
The Power Play was 2x. Wednesday's Powerball numbers were 12-17-37-58-62 and Powerball 4. ... There was one Match 5 $1 million winner in California.
Since a = n(n + 1)/2, these formulae show that for an odd power (greater than 1), the sum is a polynomial in n having factors n 2 and (n + 1) 2, while for an even power the polynomial has factors n, n + 1/2 and n + 1.