cristina89 said:
The limit of a sequence refers to the value that a sequence of numbers approaches as the number of terms in the sequence increases. It is the value that the terms of the sequence get closer and closer to, but may never actually reach.
To prove the existence of a limit of a sequence, one must show that the terms of the sequence approach a specific value as the number of terms increases. This can be done through various methods such as the epsilon-delta definition or the squeeze theorem.
The epsilon-delta definition of a limit states that for any given positive number epsilon, there exists a positive integer N such that for all terms of the sequence with an index greater than N, the distance between the term and the limit is less than epsilon.
No, a sequence can only have one limit. If a sequence has more than one limit, then it is not a convergent sequence and does not have a limit.
The limit of a sequence can be determined by analyzing the behavior of the terms of the sequence as the number of terms increases. This can be done through various methods such as finding a pattern, using mathematical formulas, or applying theorems such as the squeeze theorem.