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
SEQUENCE Difference Between Series and Sequence
First of all, when you talk about a sequence, you are simply referring 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, 6 is another type of sequence; but arranged in descending order. There are other more complicated sequences, but they also present some kind of pattern, such as 7, 6, 9, 8, 11, 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 sixth 1 / n is, they can easily answer that it is 1/6. The same pattern is followed, if you ask a person for the nth term of a millionth; which will be 1/1,000,000. This also shows that sequences have “behaviors.” In the above example of the sequence from 1 to 1/5, the behavior of the sequence moves closer and closer to the value 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.
In contrast, 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 in no particular order or pattern, but they are still added together. These make up an absolutely convergent series. However, there are also some series that result in a change in the sum by placing the terms in a different order.
Using the same example (from the 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 answer or the 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, on the other hand, 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.