Hey guys. This numerical analysis section is really throwing me. I don't quite know how to handle this order of convergence stuff. Here's just one example of a problem that's giving me trouble:

Any help would be much appreciated !Let , where and is smooth.

Suppose a sequence satisfies and converges to , where is a simple zero of . We define "order of convergence" to be the largest real number such that

exists and is nonzero. Determine the order of convergence.