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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.

29 October 2003