Firstly lets find the limit by solving
gives x = 4, so limit is 4
we can see that if then and also that
so we can conclude that the sequence decreases and has a lower bound of 4.
hope this helps and makes sense!
a) X1=8 and Xn+1=.5Xn +2 for n within naturals. Show that Xn is bounded and monotone and find the limit?
b) X1> and Xn+1=2-1/Xn for n within naturals. Show that Xn is bounded and monotone and find the limit
for part a i can say x1>x2, thus the sequence is decreasing.
Note that so that
adding 2 to both sides we get
but that means