What is the difference between finding the 'rate of convergence' and the radius of convergence'? The question I am trying to solve here is to find the rate of convergence of the ratio of Fibonacci which is $\frac{F_{n+1}}{F_n}\to \phi$. Can someone guide me to how I would find the rate of convergence of this? And also tell me what the difference between radius and rate is?
Edit: I understand the difference, but I need help finding the rate of convergence of the ratio of Fibonacci which is $\frac{F_{n+1}}{F_n}\to\phi$
Best Answer
Lets take for example the geometric sequence,
$$a_n=a_0q^n$$
The Rate of convergence is $q$
And the Radius of convergence is the values of $q$ for which: $$a_0\sum_{i=0}^{\infty}{q^i}<\infty$$ The radius in this case is $$-1<q<1$$