# Math Help - Establish formula for approximation

1. ## Establish formula for approximation

If x=a is an approximation for the equation f(x)=0, then $x=a-\frac{f(a)}{f'(a)}$ is a closer approximation, establish the formula
$x_{r+1}=x_r (2-Nx_r)$ as a method of successive approximations to the reciprocal of N.

I don't know where to begin.
Thank you

2. As an iterative formula, Newton's method takes the form,

$\displaystyle x_{n+1}=x_{n}-\frac{f(x_{n})}{f^{\prime}(x_{n})}$.

To use the method to find the reciprocal of the number $N$, you have to solve the equation

$\displaystyle \frac{1}{x}-N=0,$

in which case

$\displaystyle f(x)= \frac{1}{x}-N.$

Substitute this into the RHS of the formula and simplify.

3. how did you arrive at the $\frac{1}{x}-N=0$?
can you give me like the reason, logic behind it?
thanks!

4. Originally Posted by arze
how did you arrive at the $\frac{1}{x}-N=0$?
can you give me like the reason, logic behind it?
thanks!
If $x=1/N,$ then $1/x-N=0.$