Well, maybe. It's all a question of what the rules are.
When the answer is no:
- The series of powers of 2 is not convergent.
- The series of powers of 2 is not Cesaro summable.
When the answer is maybe yes:
- The notion of analytic continuation.
If it's sometimes true, why can't it be always true.
- The subject of 2-adic analysis.
Stepping away from the real numbers (but staying
in the real world)
- The subject of z-adic analysis.
How to imagine every power series as convergent