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, each fraction is less than 1. The product rapidly approaches zero. At
. 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 (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 , each fraction is less than 1
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...