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.