(2/14)(3/14)(4/14)(5/14)(6/14)(7/14)(8/14)(9/14... Apr 2026

) act as "decay factors," significantly reducing the product's value before the linear growth of eventually dominates the exponential growth of 14k14 to the k-th power 2. Sequence Analysis

R=Pk+1Pk=k+114cap R equals the fraction with numerator cap P sub k plus 1 end-sub and denominator cap P sub k end-fraction equals the fraction with numerator k plus 1 and denominator 14 end-fraction For all (2/14)(3/14)(4/14)(5/14)(6/14)(7/14)(8/14)(9/14...

The following graph illustrates the "U-shaped" trajectory of the sequence, highlighting the dramatic shift once the numerator surpasses the constant divisor of 14. 4. Conclusion The sequence ) act as "decay factors," significantly reducing the

The general term of the product can be expressed using factorial notation: Conclusion The sequence The general term of the

The behavior of the sequence is dictated by the ratio of successive terms:

Pk=k!14k−1cap P sub k equals the fraction with numerator k exclamation mark and denominator 14 raised to the k minus 1 power end-fraction 2.1 The Critical Threshold