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Square Roots of Integers Expressed as Infinite Series

Published online by Cambridge University Press:  03 November 2016

G. L. Camm
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Extract

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.

Type
Research Article
Information
The Mathematical Gazette , Volume 33 , Issue 304 , May 1949 , pp. 99 - 104
Copyright
Copyright © Mathematical Association 1949

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References

page 104 note * Solutions of Pell’s equation, x2 - Dy2 = ± 1, have been tabulated for all integers D up to 2000. See E. L. Ince, Cycles of Reduced Ideals in Quadratic Fields, B.A. Tables, 1934.