Let xn+1=25−2xn and x1>0
I need to show that this sequence is contractive and am having trouble.
xn is contractive ⇔ ∣xn+1−xn+2∣<r∣xn−xn+1∣, where 0<r<1. I have tried plugging in the square roots but am unable to get close to what it needs to be.
The way I'm attempting it is by starting with ∣xn+1−xn+2∣ and trying to get a series of less-than/less-than-or-equals to attain the above. I've done a few of these and they were more or less straight-forward, but I'm feeling there's a trick of some kind I can't find.
Thanks in advance,
-Daon
I need to show that this sequence is contractive and am having trouble.
xn is contractive ⇔ ∣xn+1−xn+2∣<r∣xn−xn+1∣, where 0<r<1. I have tried plugging in the square roots but am unable to get close to what it needs to be.
The way I'm attempting it is by starting with ∣xn+1−xn+2∣ and trying to get a series of less-than/less-than-or-equals to attain the above. I've done a few of these and they were more or less straight-forward, but I'm feeling there's a trick of some kind I can't find.
Thanks in advance,
-Daon