Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T07:38:18.135Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  03 November 2016

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Mathematical Notes
Copyright
Copyright © Mathematical Association 1906

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.