Hi, I have the following exercise... I have solved the first question, but I don't know about the second question. Thanks for whatever help you have give me!

Since early electronic computers had no automatic division, it was necessary to accomplish this by a process of calculating reciprocals using only addition, subtraction and multiplication.

1) Show that the Newton-Raphson method iteration function for r(x)=x^{-1}-R, where R>0, is

F(x)=x(2-Rx).

Verify that x*=R^{-1} is a fixed point of F(x).


And here is the question that I have no clue about (I don't need any help with the question above):

"2) Show further that the iteration satisfies

1-Rx_{n+1}=(1-Rx_n)^2,

and deduce that
1-Rx_{n+1}=(1-Rx_0)^{2^{n+1}}.

Hence show that Rx_n  -> 1 as n approaches infinity if and only if 0<Rx_0<2.
Deduce that x_n->R^{-1} as n approaches infinity if and only if 0<x_0<2/R.

Note: you might need to illustrate this conclusion graphically."