(2/14)(3/14)(4/14)(5/14)(6/14)(7/14)(8/14)(9/14... -
, the term is exactly 1, and the product reaches its local minimum. As
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 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 , the term is exactly 1, and the
, each fraction is less than 1. The product rapidly approaches zero. At The following graph illustrates the "U-shaped" trajectory of
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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