What is an interval, |S − S4| ≤ |R4| for which the actual sum exists?

Question

The series:  has a partial sum  when x = 1. What is an interval, |S − S₄| ≤ |R₄| for which the actual sum exists? Provide an exact answer and justify your conclusion.

Answer 1

The error will not exceed the first omitted term which is 1/9!

I intentionally answered this question with sort of a hint, because as phrased the question makes no sense.

The series given is the Maclaurin series for cosine and it converges for all values of x, i.e. the sum exists for all values of x.