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This work aims to explore the recursive decomposition of factorials using consecutive summation notation and derive a generalized formula.

May 7, 2026Open Access

Recursive Decomposition of Factorials via the Consecutive Summation Notation n_+ and the Derivation of a Generalized Formula

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This work aims to explore the recursive decomposition of factorials using consecutive summation notation and derive a generalized formula.
Utilized recursion to decompose factorials into sums based on the consecutive summation notation.
Developed mathematical expressions to represent these decompositions and explored their properties.
Presented a new generalized formula that simplifies the computation of factorials.
Demonstrated that the recursive decomposition can lead to more efficient calculations in various mathematical contexts.

Randomized trial reveals a new approach to factorial decomposition, suggesting broader applications in mathematics.

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SungKun Kim (2026) studied this question.

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