Solving Iterative Formulas: Xn+1 Explained

[DeanBH]

Homework Statement

First of all this is revision not homework =)

question is Xn+1 = Cuberoot ( 17.5-2xn)

answer lies between 2 and 3. i know the answer is 2.34 but what i don't get is why it is
xn+1 = equation, because when you put xn=2.34 into the equation you get 2.34 out.
shouldnt get 3.34 out if its xn+1. what's the purpose of the n+1!

 

[dirk_mec1]

xn and xn+1 both go (in this convergent case) to a limit call it L. Now substitute L for xn and xn+1 and solve the equation.

 

[DeanBH]

xn and xn+1 both go (in this convergent case) to a limit call it L. Now substitute L for xn and xn+1 and solve the equation.

i don't think you understand what I'm confused with,



i know the answer is 2.34 so i put it into check

xN+1 = cuberoot(17.5-2xn)

3.34=cuberoot(17.5-2*2.34)
3.34=2.34

do you understand what i don't understand.

 

[dirk_mec1]

You've made an error in your calcution it is correct.

 

[yyat]

If you mean

$$x_{n+1}=(17.5+2x_n)^{1/3}$$

then the answer is $$\lim_{n\to\infty}x_n=2.34$$, and this solution can be found as dirk_mec1 described.

But if you mean

$$x_n+1=(17.5+2x_n)^{1/3}$$

then $$x_n=1.44$$ for all $$n$$.