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

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

is a classic example of a sequence that appears to vanish but eventually explodes. While the initial terms suggest a limit of zero, the "power" of the factorial ensures that for sufficiently large , the product overcomes any constant denominator. (2/14)(3/14)(4/14)(5/14)(6/14)(7/14)(8/14)(9/14...

The behavior of the sequence is dictated by the ratio of successive terms: ), Stirling's Approximation confirms that the product will

) 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 While the initial terms suggest a limit of

. 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

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

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