(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

I have the equation:

|e_{n+1}/e_{n}^{α}| ≈ C

e_{n}= r - x_{n}

e_{n+1}= r - x_{n+1}

3. 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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# Order of Convergence: Iteration Scheme

Can you offer guidance or do you also need help?

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