One last thing. So I have this sequence:

$\displaystyle x_1:= 8 \ \mbox{and} \ x_{n+1} =\frac{1}{2}x_n + 2 \ \ \mbox{for all} \ n\in N$

I know that it is strictly decreasing, which makes it monotone, but how would I prove that?

I also think that the limit is 4 just by looking at the first few terms, which means that since it converges that it is bounded, but I don't know the proper way to prove that either. Help?

Thanks so much.