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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
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- Mathematical Notes
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- Copyright © Mathematical Association 1906
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.