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    Real Analysis - Newton's Method and showing convergence.

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    Newton's Method: Consider the equation f(x)=0 where f is a real-valued function of a real variable. Let x_0 be any initial approximation of the solution and let
    x_(n+1)=x_n - (f(x_n)/f'(x_n)).
    Show that if there is a positive number "a" such that for all x in [x_0-a, x_0+a]
    |(f(x)f''(x))/((f'(x))^2)|<=lambda<1 and
    then the sequence (x_n) converges to a solution of f(x)=0.

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    Newton's Method and convergence are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.