Hello, landlord, it shows that you are studying hard to ask such a question. Indeed, freshmen usually have such troubles when they study the limit scale in advanced mathematics. For example, a very simple equation about x can obviously be expressed by n and the value range of x can obviously be obtained when n tends to infinity, but the textbook should make this equation of n simple by scaling. First of all, the original intention of the textbook is to prove intuitively that when n is greater than a certain natural number, X will always meet the limit range to be proved, even just like the simple operation of P/N in one step, which has the advantage of giving such a natural number. Although this natural number is not necessarily the critical optimal value of n, it is definitely a qualified natural number. If the landlord only uses an expression of n without any conversion, then the relationship between x and n will be a complex operational relationship, which can not express an integer well, so it can not be proved intuitively by definition; Secondly, the method you want to use is very limited, not all equations can be expressed by pure unary functions;

Here is a simple example:

Find the limit of n-open n-degree roots

Let n root sign n times be equal to x, and find the limit of x, can n still be represented by the formula of x? Obviously impossible.

This limit must be given by monotonicity plus boundedness;

It's a little confusing The key to this kind of thing is that you need to practice more. Some things in mathematics are also puzzling. I hope I can help the landlord and wish you a high score in mathematical analysis.