The rate of convergence defined as: $$ \lim_{k\rightarrow \infty}\frac{|x_{k+1}-a|}{|x_{k}-a|} =\mu$$
seems to mean that a sequence with a higher $\mu$ should have a higher rate of convergence ie. should converge faster to its limit.
I find that the opposite is true, as for $x_{n+1}=\mu x_{n}+c$ , with$|\mu|<1$, it converges faster as $\mu$ is closer to zero.
Why such a counterintuitive definition? Am I missing something?