When is the inequality property of limit? Same topic Limxn = a > 0, find LIM (xn ^ n) / N! Are n → infinity The solution is: because xn → a, there exists n, when n > N, 0 < xn < 2a, then 0 < (xn ^ n) / N! < (2a ^ n) / N! And lim (2a ^ n) / N! = 0, so LIM (xn ^ n) / N! = 0 In fact: when I am very close, I become you.

When is the inequality property of limit? Same topic Limxn = a > 0, find LIM (xn ^ n) / N! Are n → infinity The solution is: because xn → a, there exists n, when n > N, 0 < xn < 2a, then 0 < (xn ^ n) / N! < (2a ^ n) / N! And lim (2a ^ n) / N! = 0, so LIM (xn ^ n) / N! = 0 In fact: when I am very close, I become you.

Because xn → a, there exists n. when n > N, 0 < xn < 2A. Do you mean you don't understand this?
Well, this is the nature of textbook definition!
You can also understand that xn approaches a when n is infinite. Then, xn is bound to be smaller than 2A!