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Approximations to n√1+x where n is an integer and 0<x<1

Published online by Cambridge University Press:  03 November 2016

J.M. Child
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Extract

If we seek approximations to in the form

of such a nature that the fraction gives, on performing the division, an infinite series whose first 2r+1 terms are identical with the first 2r+1 terms of the Binomial Expansion for we shall obtain 2r equations of the form

Type
Research Article
Information
The Mathematical Gazette , Volume 8 , Issue 124 , July 1916 , pp. 289 - 295
Copyright
Copyright © The Mathematical Association 1916

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References

page 293 note * By the use of the caluculus for first even convergent.

page 295 note * Taking µ=•4342944819 from Chambers. For closer approximations µ would have to be calculated from the convergents above or closer ones.