Please show that when n=1, Newtons method given by:

x^k=x^(k-1)-(J(x^(k-1))^-1)(F(x^(k-1)) for k>=1

reduces to the familiar Newton's method given by:

P_n=P_n-1 - f(p_n-1)/f'(P_n-1) for n>=1

Note:
^-1 is inverse
J is the jacobian matrix
The top equation is called newton's method for non linear systems. x is a vector. F(x_1,...,x_n)=(f_1(x_1,...,x_n),f_2(x_1,...,x_n),...,f_n(x_1,...,x_n))

Solution Summary

A Jacobian is employed in this Newton's Method proof. The solution is detailed and well presented.

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... remained consistent and capable of derivation (proof in the ... what Ptolemy did to this idea, then Newton, Galileo and ... The method that we employ will help us to ...