Sqrt[1 + z] == 1 + ContinueFraction[{(Floor[k/2] - (-1)^k (1/2)) z, (1/2) (1 - (-1)^k) k + (-1)^k + 1}, {k, 1, Infinity}] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]

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2001-10-29