To show that the sequence $a_n = 2 - \frac{1}{n}$ converges, we need to find its limit as $n$ approaches infinity.

Step 1: Identify the Sequence

The sequence is given by: $a_n = 2 - \frac{1}{n}$

Step 2: Compute the Limit

As $n$ approaches infinity, the term $\frac{1}{n}$ approaches 0. Therefore, the sequence can be analyzed as follows: $\lim_{n \to \infty} a_n = \lim_{n \to \infty} \left(2 - \frac{1}{n}\right)$ $\lim_{n \to \infty} a_n = 2 - \lim_{n \to \infty} \frac{1}{n}$ Since $\lim_{n \to \infty} \frac{1}{n} = 0$, we have: $\lim_{n \to \infty} a_n = 2 - 0 = 2$

Step 3: Conclusion

The sequence $a_n = 2 - \frac{1}{n}$ converges, and its limit is 2.

Would you like more details, or do you have any other questions?

Here are some related questions:

1. What is the definition of the limit of a sequence?
2. How does one prove that a sequence is bounded?
3. What are some other examples of sequences that converge to a constant?
4. How can you determine if a sequence diverges?
5. What is the difference between convergence and divergence?

Tip: When working with sequences, always check if the terms approach a specific value as $n$ becomes large to determine convergence.