Since you wrote " ", I'm going to assume that you mean instead.
We have the following bidirectional causal chain:
You should be able to do the rest now!
Hello, I am completely lost with this question:
Let for .
1. Show that if and only if and infer that the inequality is valid for . Conclude that is ultimately decreasing and that exists.
2. Use the fact that the subsequence also converges to to conclude that .
I see why given that , since
But that's pretty much what I got =(