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

. 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

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...

AI responses may include mistakes. For legal advice, consult a professional. Learn more As ), Stirling's Approximation confirms that the product

, the term is exactly 1, and the product reaches its local minimum. As consult a professional. Learn more

), Stirling's Approximation confirms that the product will ultimately diverge to infinity. 3. Visualization of Growth

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

) 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