- #1
NihalRi
- 134
- 12
Homework Statement
2. Relevant equation
Below is the definition of the limit superior
The Attempt at a Solution
I tried to start by considering two cases, case 1 in which the sequence does not converge and case 2 in which the sequence converges and got stuck with the second case.
I know intuitively that there exists a K such that Mk < a is the second case but I can not think of how to show this. I attempted to consider cases again, like monotone increasing, decreasing, or even use the definition of couchy sequence but was not getting anywhere. Is there a way to reach the same conclusion in my second case or is my approach for this proof completely off? I would gladly supply any additional information and would greatly appreciate any help.