Search results
Results From The WOW.Com Content Network
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ... n! = 1⋅2⋅3⋅4⋅ ⋯ ... n(n + 1)(2n + 1) / 6 : The number of stacked spheres in a pyramid with a ...
1 − 1 + 2 − 6 + 24 − 120 + ⋯. In mathematics, is a divergent series, first considered by Euler, that sums the factorials of the natural numbers with alternating signs. Despite being divergent, it can be assigned a value of approximately 0.596347 by Borel summation .
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10 , the digital root of a nonzero triangular number is always 1, 3, 6, or 9.
In mathematics, a sequence of natural numbers is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once. For example, the sequence of powers of two (1, 2, 4, 8, ...), the basis of the binary numeral system, is a complete sequence; given any natural number, we can ...
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 ]
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form . [1] The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers, [2] or rectangular numbers; [3] however, the term "rectangular number" has also been applied to the composite numbers.
In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form: where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... (sequence A000215 in the OEIS ). If 2 k + 1 is prime and k > 0, then k itself ...
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.