Problem of the Week 994
An Eerie Recursion
Define the sequence e(n) by e(1) = 0, e(2) = 1, and e(n) = e(n - 1) + (e(n - 2)/(n - 2)). What is the limit of n/e(n) as n approaches infinity?
Why is it eerie? Tune in next week?
Source: The beautiful new book, Mathematical Constants, by Stephen Finch (Cambridge Univ. Press). The result is due to B. Cloitre (2002).
© Copyright 2003 Stan Wagon. Reproduced with permission.