Osittaissummaa

Osittaissummaa is a Finnish term that translates to "partial sum" in English. It refers to the sum of a finite number of terms of a sequence or series, starting from the beginning of the sequence. For example, if you have a sequence denoted by a1, a2, a3, ..., then the first partial sum (S1) is simply a1. The second partial sum (S2) is a1 + a2. The third partial sum (S3) is a1 + a2 + a3, and so on. The nth partial sum (Sn) is the sum of the first n terms: a1 + a2 + ... + an.

The concept of partial sums is fundamental in the study of infinite series. By examining the behavior of the sequence of partial sums as the number of terms approaches infinity, mathematicians can determine whether an infinite series converges to a finite value or diverges. If the sequence of partial sums approaches a limit, the infinite series is said to converge to that limit. If the sequence of partial sums does not approach a finite limit, the series diverges. Partial sums are also used in various mathematical fields, including calculus, numerical analysis, and probability.