Let f be some given function for which we wish to find a such that

f(alpha)= 0. Suppose that the equation f(x)= 0 may be arranged into

the form x=g(x), such that for some interval (a,b) alpha is in (a,b) and

g(x) belongs to (a,b) . Further, suppose that g is differentiable with |g'(x)|</= C

for x belonging to (a,b), where C is some positive number. (Note that x=g(x)

implies that alpha=g(alpha)

please note that when i say "belonging to" i mean that symbol that looks a bit like an 'E'

Prove by induction that

|alpha-Xn| </= C^n|alpha-Xo|

thanks