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

Key Points

• 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.