Final answer:
To find the values of x for which a series converges, one must first identify the type of series and then apply the appropriate convergence test. The values of x where convergence occurs are then expressed in interval notation.
Step-by-step explanation:
The student is asking to find the values of x for which a series converges. The process of determining convergence typically involves testing the series with various mathematical tests, such as the ratio test, root test, integral test, comparison test, or others depending on the type of series.
However, the details provided include some operations on a TI-83/84 calculator and various numerical values, which seem disconnected from the context of a series convergence question. The correct approach to ascertain series convergence is not explicitly provided in the question.
Moreover, the interval notation would generally express convergence in the form of an interval where the series converges for all x-values within that interval.When checking for convergence, it is important to first identify the type of series given (such as geometric, p-series, or an alternating series) and then apply the appropriate convergence test.
After establishing the convergence criteria, the interval in which x-values lie can be written using interval notation, typically in the form (a, b) for an open interval or [a, b] for a closed interval, depending on the test's conclusions.