$\displaystyle consider \ the \ the \ sequence :$
$\displaystyle x_1=a (a \in R ) \ , \ x_{n+1}= \frac{1}{4}(1+x_n) , n \geq 1$
Determine when $\displaystyle x_n$ is increasing or decreasing , then prove the convergence of $\displaystyle x_n$
$\displaystyle consider \ the \ the \ sequence :$
$\displaystyle x_1=a (a \in R ) \ , \ x_{n+1}= \frac{1}{4}(1+x_n) , n \geq 1$
Determine when $\displaystyle x_n$ is increasing or decreasing , then prove the convergence of $\displaystyle x_n$