A convergent sequence is a sequence of numbers that approaches a single value or limit as the number of terms in the sequence increases.
To determine if a sequence is convergent or divergent, you can take the limit of the sequence as the number of terms approaches infinity. If the limit exists and is a finite number, the sequence is convergent. If the limit does not exist or is infinite, the sequence is divergent.
The limit of a convergent sequence is the number that the sequence approaches as the number of terms increases. It is denoted by the symbol "lim" followed by the sequence. For example, if the sequence is written as an, the limit would be written as limn→∞ an.
No, a convergent sequence can only have one limit. If a sequence has multiple limits, it is considered to be divergent.
A convergent sequence approaches its limit as the number of terms increases. This means that the terms in the sequence become closer and closer to the limit value, but may never actually reach it. The limit is essentially the "end goal" of the sequence.