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**slevvio** I was wondering if i could get some help with this question:

Define a sequence $\displaystyle \{x_n\}_{n=1}^{\infty}$ by $\displaystyle x_1 = 1, x_2 = \frac{1}{2}$ and$\displaystyle x_n = \frac{2x_{n-1} + x_{n-2}}{4} $for $\displaystyle n \ge 3.$ Use the Monotone Convergence Theorem to show that $\displaystyle \{x_n\}_{n=1}^{\infty}$ converges and find its limit.

Ok it is not too hard to prove by induction that $\displaystyle 0 \le x_n \le 1$. But I am having trouble proving the sequence is decreasing. I have

$\displaystyle x_{n+1} - x_{n} = \frac{2x_n + x_{n-1}}{4} - x_n = \frac {x_{n-1} - 2x_n}{4}$, but I have no guarantee that this is less than or equal to zero!

Any help would be appreciated!