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184. [I. 1.] The third approximation to the nth root of a number

Published online by Cambridge University Press:  03 November 2016

T. J. I'a. Bromwich
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Type
Mathematical Notes
Information
The Mathematical Gazette , Volume 3 , Issue 55 , January 1906 , pp. 275 - 276
Copyright
Copyright © Mathematical Association 1906

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References

page 275 note * To reduce this to the form given, write x = N/an, and multiply both sides by a.

page 276 note * If a, b, n are all greater than 1, an−bn>n(a-b). This is obvious on division if n is an integer ; if n is not an integer we have

if x>l. Thus xn−l>n(x−l). Write x=a/b, and the result follows.