I have attached the actual problem as a picture (hope that is ok).
Xn+1 = 12/(1+Xn), r=3
For each of the following iteration schemes the sequence xn will converge to the given value of r provided the
initial value x0 is sufficiently close to r. In each case determine the order of convergence.
I have the equation:
|en+1/enα| ≈ C
en = r - xn
en+1 = r - xn+1
The Attempt at a Solution
I have attempted to substitute xn+1 into the last equation and then divided terms, but I end up with a final result of 3/(1+xn). I cannot understand how to find the order of convergence from this. Any hints would be appreciated.
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