The series are ordered sequences of elements They maintain a relationship with each other. Finite , meanwhile, is what has limit or end .
As you can see when analyzing these definitions, a finite series is a succession that has an end . This characteristic differentiates finite series from infinite series , which do not have an end (and, therefore, can extend or extend indefinitely).
If we think of one numerical series (a series composed of numbers ), we can find many examples of finite series. These series have a first and last term that are already defined .
Precisely this underlined feature is what establishes that there is a notable difference from the so-called finite series in terms of the infinite series. And the latter is characterized by the fact that it has no end, hence, for example, in it and in any of its type it is essential to proceed to make use of strong mathematical analysis tools to understand them, especially.
Thus, if we take a numerical series formed by the positive single-digit even numbers , we will find that it is a finite series whose components are 2, 4, 6 and 8 . The series is finite since the first positive number even is 2 and the last single digit single positive number is 8 . The rest of the even numbers (10 , 12 , 14 ...) have more than one digit and, therefore, do not correspond to the numerical series mentioned.
In addition to all of the above, we cannot ignore the fact that there is another important list of aspects regarding finite series that are worth knowing and understanding. We are referring, for example, to the following:
-They become fundamental pieces of fields such as mathematics, in each and every one of its branches and areas, whether they are integral calculations, applied mathematics, algorithms, powers ...
-In all the finite series, what is called reason plays an essential role. And it is that this is the one that is responsible for establishing the pattern that identifies the succession of numbers and, therefore, helps us know which number should continue in one of those series. Thus, for example, if we have a series 2, 4, 8 and 16, we must know that its reason is that a number gives the following when multiplying by 2. Hence, after 16, to continue the series, it must be the 32
Finite series can also be descending . A finite series descending from positive numbers multiples of 3 that has the largest number at 15 It will be as follows: 15, 12, 9, 6 and 3 .
In the case of 0 , the number usually lends itself to confusion. He 0 It is considered as a even number since it meets the condition from parity : any integer that is a multiple of 2 is even (2 x 0 = 0 ). On the other hand the 0 it is not usually described as a positive number , but is considered as a neutral number . That is why it is not part of the finite series that we mentioned as examples .