Show that the Bisection Method converges linearly with K = 1/2
Note that x(sub n) converges to the exact root r with an order of convergence p if:
lim(n->oo) (|r - x(n + 1)|) / (|r - x(n)|^p) = lim(n->oo) (|e(n + 1)|) / (|e(n)|^p) = K
The Attempt at a Solution
EDIT: I can rearrange the equation above as follows (K = 1/2):
|e(n+1)| = 1/2|e(n)|^p
and I know that the bisection method is a linear operation, reducing the interval by 1/2 each time and converging on the real root, so p = 1, but I'm not sure how to show this?