Final answer:
The correct definition of a partial sum of the series is option B: Sm = ∑ k=m to infinity of ak, which sums the series starting with the m-th term to infinity.
Step-by-step explanation:
The partial sum of the series ∑ k=m to infinity of ak is defined as the sum of the first m terms of an infinite series. When we look at the options provided, option B is the correct definition of a partial sum: Sm = ∑ k=m to [infinity] ak. This represents the sum of the series starting from the m-th term and including all the subsequent terms up to infinity. In contrast, the other options represent either a finite series or in the case of option D, the entire series.
It is important to note, though, that when we discuss the central limit theorem, we are talking about a principle in statistics that relates to large samples, their sums, and how these sums form a distribution that approaches a normal distribution as sample size increases. However, this may not necessarily pertain to the calculation of a partial sum of a series in the context of this question.