A partial sum refers to the sum of a specific number of terms from a sequence or series. For example, in the sequence of natural numbers 1, 2, 3, 4, ..., the partial sum of the first three terms is 1 + 2 + 3 = 6. Partial sums are useful in various mathematical contexts, including calculus and number theory, as they help in understanding the behavior of sequences. In the context of an infinite series, a partial sum can be used to approximate the total sum of the series. As more terms are added, the partial sum may converge to a specific value. For instance, in the series 1/2, 1/4, 1/8, ..., the partial sums approach 1 as more terms are included, illustrating how partial sums can provide insight into the overall sum of a series.