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Math Series

  1. Jan 4, 2012 #1
    1. The problem statement, all variables and given/known data

    [tex]U_{n+1}=\sqrt{12+U_{n}}[/tex] V0=0


    2. Relevant equations
    1) prove that Un<4
    2) prove that [tex]4-U_{n+1}\leq\frac{1}{4}(4-U_{n})[/tex]
    3) conclude that 4-Un<(1/4)^(n-1)


    3. The attempt at a solution

    1- for n=0 0<4
    assume Un<4 for some n in N and prove that Un+1<4

    √(12+Un)<4 then square both sides and we get:

    12+Un<16 then Un<4
    so for every n in N: Un<4

    2) I don't know what to do any help?
     
  2. jcsd
  3. Jan 4, 2012 #2
    2) I don't know what to do any help?

    Have you tried substituting √(12+Un) for U(n+1) in [tex]4-U_{n+1}\leq\frac{1}{4}(4-U_{n})[/tex] and then evaluating the resulting expression for the largest possible value of U(n+1)?
     
  4. Jan 4, 2012 #3
    Yea i just did that thanx for your help
     
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