cathy said:Homework Statement
an= (n/n+2)^nThe Attempt at a Solution
I was told this was convergent and I need to find the limit of the sequence. How do I do this, as I seem to keep getting that this is divergent. Isn't it divergent to infinity? Or am I missing something?
A convergent sequence is a sequence of numbers that approaches a specific value as the sequence goes on. This value is known as the limit of the sequence.
The limit of a convergent sequence can be determined by looking at the pattern of the numbers in the sequence and finding the number that the sequence approaches as it goes on. This number is the limit of the sequence.
If a convergent sequence does not have a limit, it is known as a divergent sequence. This means that the sequence does not approach a specific value as it goes on, and instead, the numbers in the sequence become increasingly larger or smaller.
No, a convergent sequence can only have one limit. If a sequence has multiple limits, it is not a convergent sequence.
The limits of convergent sequences are important in mathematics and science because they help us understand the behavior of sequences and how they approach a specific value. They are also used in calculus to define the concept of continuity and to calculate integrals and derivatives.