**Inventory021: Probability about a sequence **(proposed by Roger
Cuculière, 2/11/03).

Let u_{n} be a real sequence defined by : 0<=u_{0}<=1,
0<=u_{1}<=1, and for n>=2 : u_{n}=(sqrt(u_{n-1})+sqrt(u_{n-2}))/2.

Prove that the sequence (u_{n}), n>=4, is non-discreasing.

If u_{0} and u_{1} are choosen at random, uniformely and independantly
in [0,1], find the probability that the sequence (u_{n}) is non-discreasing
respectively for : n>=0, n>=1, n>=2, n>=3.

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