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Consider infinite sequences \{x_n\} of positive reals such that x_0=1 and x_0\ge x_1\ge x_2\ge\ldots.

a) Prove that for every such sequence there is an n\ge1 such that: {x_0^2\over x_1}+{x_1^2\over x_2}+\ldots+{x_{n-1}^2\over x_n}\ge3.999.

b) Find such a sequence such that for all n: {x_0^2\over x_1}+{x_1^2\over x_2}+\ldots+{x_{n-1}^2\over x_n}<4.

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