https://file.aiquickdraw.com/mathbot/file/1726687549588lkoztzc6.jpg

Let's solve the problem shown in the image. The given sequence is defined as follows:

\[
\{ 2, \frac{4}{3}, 1, \frac{4}{5}, \frac{2}{3}, \ldots \}
\]
which is represented by the function:

\[
f(n) = \frac{4}{n}, \quad \text{for } n = 1, 2, 3, \ldots
\]

The goal is to find the limit of this sequence as \( n \to \infty \).

### Limit of the Sequence

We are tasked with finding:

\[
\lim_{n \to \infty} \frac{4}{n}
\]

As \( n \to \infty \), the denominator \( n \) becomes infinitely large. Thus:

\[
\lim_{n \to \infty} \frac{4}{n} = 0
\]

### Conclusion

The limit of the sequence as \( n \to \infty \) is **0**.

---

Would you like further details on sequences, or do you have any questions?

Here are some related questions you might find helpful:
1. What are the key properties of converging sequences?
2. How can we determine if a sequence diverges?
3. Can you provide examples of sequences that do not have limits?
4. How do you calculate the limit of a more complex sequence?
5. What is the significance of the limit of a sequence in real-world applications?

**Tip:** Always check if a sequence is bounded and monotonic; these properties help determine if it converges.

Find the limit of the sequence {2, 4/3, 1, 4/5, 2/3, ...} where f(n) = 4/n for n = 1, 2, 3, ... as n approaches infinity.

Solve the problem of finding the limit of the sequence {2, 4/3, 1, 4/5, 2/3, ...} defined by f(n) = 4/n as n approaches infinity. This solution includes key concepts from sequences, limits, and infinity, suitable for high school or early college students.

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