Question

Let \(\sum_{n=1}^{\infty}a_n\) be any series of real numbers, then which of the following statement is true?

• A. If $\sum_{\text{n}=1}^{\infty} \text{a}_\text{n}$ is absolutely convergent then it is convergent
• B. If $\sum_{\text{n}=1}^{\infty} \text{a}_\text{n}$ is convergent then it is absolutely convergent
• C. If $\sum_{\text{n}=1}^{\infty} \text{a}_\text{n}$ is absolutely convergent then it is conditionally convergent
• D. If $\sum_{\text{n}=1}^{\infty} \text{a}_\text{n}$ is conditionally convergent then it is absolutely convergent

Hint:

Absolute Convergence $\implies$ Ordinary Convergence.
Ordinary Convergence $\kern-0.3em\not\kern-0.3em\implies$ Absolute Convergence (as shown by conditionally convergent series like \( \sum \frac{(-1)^n}{n} \)).

Answer 1

The Correct Option is A