Limits of convergent sequences

In summary, the conversation discusses the convergence of the sequence an= (n/n+2)^n and finding its limit. The poster is confused about whether it is divergent or convergent, and another user suggests that it has a finite limit as a sequence but is divergent as a series. The poster then clarifies that they have posted the same question twice.
  • #1
cathy
90
0

Homework Statement



an= (n/n+2)^n


The 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?
 
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  • #2
cathy said:

Homework Statement



an= (n/n+2)^n

The 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?

It has a finite limit as a sequence. If you are treating it as a series, it's divergent. How are you concluding it's divergent? Ah, I see this is a double post.
 
Last edited:

Related to Limits of convergent sequences

What is a convergent sequence?

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.

How do you determine the limit of a convergent 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.

What happens if a convergent sequence does not have a limit?

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.

Can a convergent sequence have multiple limits?

No, a convergent sequence can only have one limit. If a sequence has multiple limits, it is not a convergent sequence.

What is the significance of the limits of convergent sequences?

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.

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