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  2. Empty sum - Wikipedia

    en.wikipedia.org/wiki/Empty_sum

    In mathematics, an empty sum, or nullary sum, [1] is a summation where the number of terms is zero. The natural way to extend non-empty sums [ 2 ] is to let the empty sum be the additive identity . Let a 1 {\displaystyle a_{1}} , a 2 {\displaystyle a_{2}} , a 3 {\displaystyle a_{3}} , ... be a sequence of numbers, and let

  3. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    Summation of a sequence of only one summand results in the summand itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elements of a sequence are defined, through a regular pattern, as a function of their place in the sequence. For simple patterns, summation of long sequences may be ...

  4. Sequence - Wikipedia

    en.wikipedia.org/wiki/Sequence

    The empty sequence ( ) is included in most notions of sequence. ... The Fibonacci numbers comprise the integer sequence whose elements are the sum of the previous two ...

  5. Composition (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Composition_(combinatorics)

    Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same integer partition of that number. Every integer has finitely many distinct compositions. Negative numbers do not have any compositions, but 0 has one composition, the empty sequence.

  6. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    (If order matters, the sum becomes a composition.) For example, 4 can be partitioned in five distinct ways: 4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1. The only partition of zero is the empty sum, having no parts.

  7. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence. ... with T(0) = 0 (empty sum). A000292: Square pyramidal ...

  8. List of sums of reciprocals - Wikipedia

    en.wikipedia.org/wiki/List_of_sums_of_reciprocals

    The sum of the reciprocals of the numbers in any sum-free sequence is less than 2.8570 . The sum of the reciprocals of the heptagonal numbers converges to a known value that is not only irrational but also transcendental, and for which there exists a complicated formula.

  9. Empty product - Wikipedia

    en.wikipedia.org/wiki/Empty_product

    In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors.It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.