question archive Let {x_n} be a sequence of positive numbers and suppose that he sequence {x_n+1/x_n} converges to L

Let {x_n} be a sequence of positive numbers and suppose that he sequence {x_n+1/x_n} converges to L

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Let {x_n} be a sequence of positive numbers and suppose that he sequence {x_n+1/x_n} converges to L.

Suppose L <1. Prove that the sequence {x_n} converges to 0.

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