I must consider the iteration x_{n+1}=x_n - \frac{f(x_n)}{f'(x_0)}. I must find the constants C and s such that e_{n+1}=Ce_n ^s.
Where e_n=x_n-r and r is the root of f.

My attempt: e_{n+1}=x_{n+1}-r=x_n-\frac{f(x_n)}{f'(x_0)}-r=e_n-\frac{f(x_n ) }{f' (x_0 )}.

So I must rewrite e_n-\frac{f(x_n ) }{f' (x_0 )} as C e_n ^s. Thus I think I must relate e_n to \frac{f(x_n)}{f(x_0)} but I don't know how to proceed.
Any idea?
Thank you.