A convergent sequence is a sequence of numbers that approaches a specific value as the index approaches infinity. In other words, as the sequence continues, the terms get closer and closer to a single limit.
In order to search for a particular kind of convergent sequence, you must first determine what type of sequence you are looking for (i.e. arithmetic, geometric, etc.). Then, you can use various mathematical techniques such as algebraic manipulation or graphing to find the specific sequence that meets your desired criteria.
A convergent sequence has a single limit, meaning that all terms in the sequence approach the same value as the index increases. Additionally, the terms in a convergent sequence must get closer and closer to the limit as the index increases.
No, a convergent sequence cannot have a limit of infinity. The limit of a convergent sequence must be a real number, meaning that the terms in the sequence must approach a specific value as the index increases.
A convergent sequence approaches a specific value as the index increases, while a divergent sequence does not have a single limit and the terms may either increase or decrease without approaching a specific value. Additionally, a convergent sequence must have terms that get closer and closer to the limit, while a divergent sequence may have terms that increase or decrease without any pattern.