  As is well-known, the ratio of adjacent Fibonacci numbers tends to phi = (1 +
sqrt(5))/2, and the ratio of adjacent Tribonacci numbers (where each term is
the sum of the three preceding numbers) tends to the real root eta of X^3 - X^2
- X - 1 = 0. Letting alpha(n) denote the corresponding ratio for the
generalized Fibonacci numbers, where each term is the sum of the n preceding,
we obtain rapidly converging series for alpha(n), 1/alpha(n), and
1/(2-alpha(n)).
