Question

The series $\sum_{n=1}^\infty (-1)^n \frac{1}{n^2}$ is}

• A. Conditionally convergent
• B. Absolutely convergent
• C. Oscillatory
• D. Divergent

Hint:

To distinguish between convergence types:
- \(\sum (-1)^n \frac{1}{n}\) is Conditionally Convergent (because \(\sum \frac{1}{n}\) diverges, but the alternating series converges).
- \(\sum (-1)^n \frac{1}{n^2}\) is Absolutely Convergent (because the absolute series \(\sum \frac{1}{n^2}\) converges).

Answer 1

The Correct Option is B