I have an exercise to prove something in contraction mapping
I think it is easy but I'm not familiar with the subject.
It is REALLY urgent
The first problem is quite straightforward: Let , and notice that . (This is by definition of the sequence .) In fact, it's easy to see that by induction for . So by the triangle inequality
Letting gives us .
(Here we have used the identity of a geometric series.)
I have no idea how to do the second problem, sorry.