Series vs. Sequence
Difference between Series and Sequence: – The terms “series” and “sequence” are used interchangeably in common and informal practice. However, they are very different concepts from each other; especially with regard to scientific and mathematical points of view.
Difference between Series and Sequence
First of all, when talking about a sequence, it simply refers to a list of numbers or terms. In this case, the order of the numbers in the list is of particular importance. It must be logical. For example, 6, 7, 8, 9, 10 is a sequence of numbers from 6 to 10 in ascending order. The sequence of 10, 9, 8, 7, and 6 is another type of sequence; but arranged in descending order. There are other more complicated sequences, but they also have some kind of pattern, such as 7, 6, 9, 8, 11, and 10.
In the sequence there is always a pattern. For example, 1, 1/2, 1/3, 1/4, 1/5 and so on, if you ask someone what the 6th 1 / n is, you can easily respond that it is 1/6. The same pattern is followed, if a person is asked for the nth term of a millionth; which will be 1/1, 000,000. This also demonstrates that the sequences have “behaviors”. In the previous example of sequence 1 through 1/5, the behavior of the sequence moves closer and closer to zero. Since there is no negative value or any number less than zero in this sequence, the limit or end is assumed to be zero.
On the contrary, a series simply consists of adding or adding a group of numbers (for example, 6 + 7 + 8 + 9 + 10). Therefore, a series has a sequence with mentions (variables or constants) that are added. In a series, the order of appearance of each term is also important, but not always; just like in a sequence. This is because some series may have terms without a particular order or pattern, but still they are added together. These form an absolutely convergent series. However, there are also some series that give rise to a change in the sum by placing the terms in a different order.
Using the same example (from sequence 1 to 1/5), if we associate it with a series; we could immediately say 1 + 1/2 + 1/3 + 1/4 + 1/5 and so on. If the response or sum of the series is very high, the infinity symbol is placed, or more appropriately qualified, as divergent.
Key differences between Series and Sequence
- In the sequence the sum is not important, as opposed to the series; in which it is.
- In the sequence it is important that there is always an order or pattern, but in the series this is not absolutely necessary.
- A sequence is a list of numbers or terms, while a series is a sum of numbers.