# Math Help - newton referson question..

1. ## newton referson question..

find 2000 in the power of 1/3
the formula of newton referson is

$x_{n+1}=\frac{2}{3}(x_n+\frac{1000}{x_n^2})$
how to know what x_0 to choose for this formula
??

because when i put x_0=1 i have many steps
but when x_0=10 i have only 4

??

2. There is no fixed way to determine the best value of $x_0$ except that it should be close to the correct answer- and of course you don't know what the correct answer is! If you know that the third root of 1000 is 10, you should be able to guess that the third root of 2000= $\sqrt[3]{2}(10)$ is going to be close to 10.

3. thanks