Suppose I am looking for the root of a function of the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(x)=x ^{m}-c[/tex], where c,m>1.

Suppose I take my first guess to be [tex]x _{0}=c[/tex].

Then using newtons method my next guess will be given by:

[tex]x _{n+1}=x _{n} - \frac {f(x _{n})}{f'(x _{n})}[/tex].

From this, or thinking about this graphically it is obvoius that

[tex]x _{0}>x _{1}>x _{n}>x _{n+1}>c^{1/m}[/tex].

However I don't know how should I go about formally proving this.

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# First step to proof of convergance using Newton's root finding method

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