Convergence of sequences refers to the property of a sequence of numbers where its terms approach a fixed limit as the number of terms increases.
To prove that a sequence is convergent, you must show that as the number of terms increases, the terms get closer and closer to a fixed limit. This can be done by using the definition of convergence and showing that the sequence satisfies the conditions for convergence.
Convergence and divergence of sequences are opposite properties. A convergent sequence approaches a fixed limit, while a divergent sequence does not have a fixed limit and its terms may either increase or decrease without bound.
No, a sequence can only have one limit. If a sequence has multiple limits, then it is not a convergent sequence.
Some common methods used to determine the convergence of a sequence include using the definition of convergence, the squeeze theorem, and various convergence tests such as the ratio test or the root test.