Please see the attached file for the full problem description.
Given Sn and S∈ (0,∞).
If Sn →S, prove ∃α>0, ∃N∈N s.t. ∀n ≥ N, an>α.
There is a small mistake in your problem.
The problem should be like this:
Given Sn and S in (0,infinity). If Sn approaches ...
A sequence proof is provided. The proof is concise.