# Differences between series and succession

The terms series and succession are applied in mathematics to a set of elements that follow a certain order. On many occasions they are terms that must be studied first to understand their meaning and application. That is why, in this article, we will present both definitions briefly and then point out the differences that exist between both terms, so that readers understand what it is about when talking about each of them and can make proper use of them. the same.

## Serie

It can be said that a series is defined as the sum of a set of terms that correspond to a sequence. Also, a series can have a sequence with mentions (variables or constants) that are added and this can be finite or infinite. In addition to this, the series are usually written with the Greek symbol Σ which is read as -sum-.

There are different types of series among which are mentioned:

• Geometric series : is one where each term is equal to the previous one multiplied by a constant.
• Divergent series : is one where the infinite sequence of the partial sums of the series does not have a limit.
• Convergent series : is one where the infinite sequence of the partial sums of the series has a limit).
• Alternate series : one whose terms are alternately positive and negative.
• Power series : one where the added elements make up a power.
• Telescopic series: that series whose partial sums have a fixed number of terms after their cancellation.

For example:

Series 1: 6 + 7 + 8 + 9 + 10 = 40

Series 2: ∑=1+4+7+10+13+…

## Succession

A sequence is defined as a set of elements arranged in an orderly way, that is, they are ordered sequences of elements (numbers) that have as a common characteristic that their predecessor has the same quality or difference between one and the next.

Sequences can be finite or infinite, so it is finite if it has a term or end and it is infinite if it does not have an end. In addition, sequences have as their main characteristic that they always follow a pattern, whether it is more or less complicated.

There are different types of sequences, among which are:

• Arithmetic sequences : is one where the difference between one term and the next is a constant.
• Geometric sequence : one where each term is calculated by multiplying the previous one by a fixed number.
• Ascending or increasing succession: one that goes from a lower value to a higher value.
• Descending or decreasing succession: one that goes from a higher value to a lower value.

For example:

Sequence 1 : 1, 4, 7, 10, 13, 16, 19, 22, 25 (se

Sequence 2 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65…

Once the above terms have been defined, it can be said that the main differences between series and succession are:

• The series are a numerical sequence linked by basic mathematical operations such as addition (by summation) while the sequences are numbers arranged in a certain order without mathematical operation.
• In the series, the order is not so relevant, since it is not always a list that follows a certain pattern, while in the sequence, the order is relevant because it determines the pattern to follow or the limit of the sequence.
• You can find constants or variables in a series.