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Homework Statement
I have attached the actual problem as a picture (hope that is ok).
X_{n+1} = 12/(1+X_{n}), r=3
For each of the following iteration schemes the sequence x_{n} will converge to the given value of r provided the
initial value x_{0} is sufficiently close to r. In each case determine the order of convergence.
Homework Equations
I have the equation:
e_{n+1}/e_{n}^{α} ≈ C
e_{n} = r  x_{n}
e_{n+1} = r  x_{n+1}
The Attempt at a Solution
I have attempted to substitute x_{n+1} into the last equation and then divided terms, but I end up with a final result of 3/(1+x_{n}). I cannot understand how to find the order of convergence from this. Any hints would be appreciated.
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