The lower right n represents the relationship between the number to be brought in and this series.
You should understand this, right? …
You can also take a look at this:
General term formula of series: If the relationship between the nth term of series and n can be expressed by a formula, then this formula is called the general term formula of this series.
Note: (1) Not all series can write their general formula, such as the above series ④;
(2) The general formula of series is sometimes not unique. For example, the general formula of series: 1, 0, 1, 0, 1, 0, … can be any one.
⑶ The function of the general term formula of series: ① Find any term in the series; Test whether a number is an item in a sequence.
From the perspective of mapping and function, a sequence can also be regarded as a positive integer set N* (or its finite set {1, 2,3, ..., n}). When the independent variable takes the value from small to large, a series of corresponding function values, and the general term formula of the sequence is the analytical formula of the corresponding function.
For the function, we can draw its corresponding image according to its resolution function. It seems that the sequence can also draw its corresponding image according to its general formula. Let's practice drawing images of series ① and ②, and summarize their characteristics.
When drawing, for convenience, the unit length on the two coordinate axes of rectangular coordinate system can be different. The images of series ① and ② are shown in figure 1 and figure 2 respectively.
5. The images in this series are all a set of isolated points.
6. There are three representations of series:
Enumeration method, general formula method and image method.
7. Finite series: series with finite terms. For example, the sequence ① is a finite sequence.
8. Infinite series: series with infinite terms. For example, the series ②, ③, ④, ⑤ and ⑤ are infinite series.
This is the series mentioned above.
4,5,6,7,8,9, 10.①
1, , , , ,….②
1,0. 1,0.0 1,0.00 1,0.000 1,….③
1, 1.4, 1.4 1, 1.4 14,….④
- 1, 1,- 1, 1,- 1, 1,….⑤
2,2,2,2,2,….⑥