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

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.

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

, each fraction is less than 1. The product rapidly approaches zero. At is a classic example of a sequence that

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 Sequence Analysis , each fraction is less than 1

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

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