Abstract
It is Well known that square roots of integers and rational numbers can be calculated by means of recurrence relations. Further, the same recurrence relations can sometimes be used to express a square root as a continued fraction. From a certain type of recurrence relation which gives a square root it is also possible to express that root as a rapidly convergent infinite series. As might be expected, the method is connected with the theory of continued fractions, and that connection will be given.
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