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Thread: convergent and the limit

  1. #1
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    convergent and the limit

    $\displaystyle consider \ the \ the \ sequence :$
    $\displaystyle x_1=a (a \in R ) \ , \ x_{n+1}= \frac{1}{4}(1+x_n) , n \geq 1$
    Determine when $\displaystyle x_n$ is increasing or decreasing , then prove the convergence of $\displaystyle x_n$
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  2. #2
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    true or not ???

    if $\displaystyle a > \frac{1}{3} \ then \ x_n \ is \ decreasing$
    if $\displaystyle a < \frac{1}{3} \ then \ x_n \ is \ increasing$
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