Question

Let $\sum_{n=1}^\infty a_n$ is absolutely convergent series, then}

• A. $\sum_{n=1}^\infty a_n$ is convergent
• B. $\sum_{n=1}^\infty a_n$ is conditionally convergent
• C. $\sum_{n=1}^\infty a_n$ is not convergent
• D. $\sum_{n=1}^\infty a_n$ is oscillatory

Hint:

Remember the direction of this logical implication:
- Absolute Convergence \(\implies\) Convergence (always true).
- The reverse is not always true: a series can converge without converging absolutely (which defines Conditional Convergence).

Answer 1

The Correct Option is A