In mathematics, terms are used as synonyms when in reality they are different numerical executions. In the case of the sequence as a finite order of elements, for its part, the mathematical series uses sequences giving value and result to the operation.
It is a mathematical application in which natural numbers are used and at the same time resources are required to complement them, being numbers of other natures, geometric figures, or functions. Each of the elements used is called succession terms, and their ordering is called length. The order in which the terms appear is relevant to obtaining the correct length.
It is taken into consideration that a term can appear more than once in the achievement, but without losing the structure of the succession.
A series is considered the applied sum of a mathematical sequence. It is the action and result of the sum of terms united in sets, which give way to the growth of the sequence from finite to infinite, becoming a series, having a convergence of the terms, that is, following the same order from beginning to end. The series uses the summation symbol to distribute the quantities of terms to be used, as well as for the exact distribution of the set of elements of the same sequence.
Difference between sequence and Series
- The mathematical sequence integrates natural numbers, geometric figures, and functions in a particular way.
- The series unites the mathematical elements to be used and distributes them through sets that will be added later.
- The order of the elements in the sequence is relevant.
- The series is an infinite numerical sequence and the order of the elements is not so important to obtain the summation value.
- The series is a sum of sequences, while the sequence is a finite list or established set of elements.
- In succession, there is always a pattern from start to finish, not necessarily in series.