The question is asking whether the sequence $f_n = \frac{(-1)^n}{n}$ converges.

To determine the convergence of this sequence, let's analyze the general behavior of $f_n = \frac{(-1)^n}{n}$.

Solution:

1. The term $(-1)^n$ alternates between $1$ and $-1$, so the sequence oscillates in sign.
2. However, as $n$ increases, the term $\frac{1}{n}$ tends to $0$.
3. Since $f_n$ is of the form $\frac{(-1)^n}{n}$, the oscillations get smaller as $n$ grows because $\frac{1}{n} \to 0$.

Therefore, despite the oscillation in signs, the sequence converges to $0$ as $n \to \infty$.

Conclusion:

The answer to the question is:

• a. Ja (Yes)

Would you like a more detailed explanation of the convergence?

Here are 5 related questions to expand your understanding:

1. What is the difference between absolute and conditional convergence?
2. How does the behavior of an alternating sequence differ from a non-alternating one in terms of convergence?
3. What is the definition of convergence for a sequence?
4. What is the general method to test if a sequence converges to zero?
5. How would the convergence change if the sequence was $\frac{1}{n^2}$ instead of $\frac{(-1)^n}{n}$?

Tip: To test for convergence, observe the behavior of the sequence as $n$ approaches infinity.