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Iterative formulas

  1. Mar 5, 2009 #1
    1. The problem statement, all variables and given/known data

    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. whats the purpose of the n+1!!
     
  2. jcsd
  3. Mar 5, 2009 #2
    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.
     
  4. Mar 5, 2009 #3
    i don't think you understand what i'm confused with,



    i know the answer is 2.34 so i put it in to check

    xN+1 = cuberoot(17.5-2xn)

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

    do you understand what i dont understand.
     
  5. Mar 5, 2009 #4
    You've made an error in your calcution it is correct.
     
  6. Mar 5, 2009 #5
    If you mean

    [tex]x_{n+1}=(17.5+2x_n)^{1/3}[/tex]

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

    But if you mean

    [tex]x_n+1=(17.5+2x_n)^{1/3}[/tex]

    then [tex]x_n=1.44[/tex] for all [tex]n[/tex].
     
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