(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

), Stirling's Approximation confirms that the product will ultimately diverge to infinity. 3. Visualization of Growth (2/14)(3/14)(4/14)(5/14)(6/14)(7/14)(8/14)(9/14...

increases beyond 14, each new term is greater than 1. Because the numerator grows factorially ( ) while the denominator grows exponentially ( 14k14 to the k-th power The following graph illustrates the "U-shaped" trajectory of

, the term is exactly 1, and the product reaches its local minimum. As the term is exactly 1

. We analyze the transition point where the sequence shifts from monotonic decay to rapid divergence and discuss the number-theoretic implications of the denominator's primality relative to the numerator's growth. 1. Introduction

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