On N > N in sequence limit For example, if the sequence is n + 1 / N and the limit is 1, 1 / N can be calculated If you want the distance between the sequence and the limit to be less than 0.001, as long as n > 2000 In the concept of limit, there is an n > N, that is, 2001 > 2000 What does this n stand for?

On N > N in sequence limit For example, if the sequence is n + 1 / N and the limit is 1, 1 / N can be calculated If you want the distance between the sequence and the limit to be less than 0.001, as long as n > 2000 In the concept of limit, there is an n > N, that is, 2001 > 2000 What does this n stand for?

I'll explain the definition of limit to you in vernacular
For the limit of sequence:
Mathematical expression: if there is a positive integer n for any ε > 0, such that when n > N, | an-a | ∞) an = a
Vernacular expression: if the distance between all items of the sequence after the foot item and a can be arbitrarily small
The sequence is said to converge to a, denoted as LIM (n - > ∞) an = a
That is to say, I'll give you a small distance ε, then you start from the first term until you find that all the items after the nth term are less than ε from a, then this n and all the subsequent n are the desired n, which is just the subscript of several terms

[2 - (1 + x) ^ n] = 2 find the range of x [sequence limit]

I came out to ask the questions before I wrote them clearly
Does n tend to positive infinity? If not, there is no solution
When n approaches positive infinity, LIM (1 + x) ^ n = 0, so | 1 + X|

When does limit proof of sequence need scaling
I did two questions, one is 1 / N2
I mean the limit proof in advanced mathematics, not the proof of sequence
It's the simplest limit proof. I'll give you a general formula of a sequence and tell you its limit. I'll let you prove that it's the limit. At this time, when simplifying the formula containing N and E, you may need to scale. I just don't know the rules of scaling here

In limit, we should make clear the concept of order under limit process
This order can be used to divide infinitesimal function and its equivalent function, some similar to the rank of matrix
Some of these equivalent functions are representative functions, which are easy to understand. Therefore, the non representative functions should be expanded and shrunk, and close to these functions. Those elementary functions are equivalent in order, so we need to make a summary in the question, or we can learn from them and then master them. The key is to find these representative functions
Some inequalities are very common, such as SiNx. Therefore, we should master these types. When it comes to representative functions, we should also expand and shrink them
The special case of limit function is the sequence of limit function
For example: 1 / N -- > 0, sin (1 / N) - > 0 is similar to SiNx -- > 0 (X -- > 0)
For example: when X -- > 0, 2x -- > 0 and 3x -- > 0 have a range
Six basic elementary functions, in the same limit process,
The x power of E is equivalent to SiNx and sin2x
Therefore, it is necessary to grasp the infinitesimal representation of different high powers of X in different limit processes, and then get close to each other
In general, the expansion and contraction are towards polynomial function, but they can't be the same