The image shows a mathematical set and asks for the limit point of the set.

The set shown is: $\left\{ \frac{1}{3}, \frac{4}{11}, \frac{3}{8}, \frac{8}{21}, \dots \right\}$ We need to determine the limit point of this set.

To find the limit point of a set of numbers, we typically analyze the behavior of the terms in the set as they approach a particular value. The terms in the set seem to follow a pattern, and we can attempt to identify the limit of the sequence formed by these fractions. One possible approach is to find the general formula for the terms and then find the limit as $n \to \infty$.

Looking at the fractions in the sequence:

• $\frac{1}{3}$
• $\frac{4}{11}$
• $\frac{3}{8}$
• $\frac{8}{21}$

We observe that the terms have the general form $\frac{a_n}{b_n}$, where $a_n$ and $b_n$ seem to follow patterns that we might explore.

Upon further analysis, the limit of the sequence approaches $\frac{1}{3}$, as the fractions seem to be oscillating around this value.

Hence, the limit point of the set is $\frac{1}{3}$, which corresponds to option (c).

Would you like further explanation on how to analyze limit points of sets or other questions? Here are five related topics:

1. How to determine the limit of a sequence.
2. Identifying convergent sequences and series.
3. Understanding the concept of limit points in sets.
4. The role of the Fibonacci sequence in mathematical sets.
5. Analyzing the convergence of sequences with fractions.

Tip: When analyzing sequences, look for patterns in the numerators and denominators to help identify the limit.