Question

Let ($\text{a}_\text{n}$) and ($\text{b}_\text{n}$) are two convergent sequences of real numbers, then which of the following is always true ?

• A. ($\text{a}_\text{n}$) + ($\text{b}_\text{n}$) is convergent
• B. $\frac{(\text{a}_\text{n})}{(\text{b}_\text{n})}$ is always divergent
• C. $\frac{(\text{b}_\text{n})}{(\text{a}_\text{n})}$ is always convergent
• D. ($\text{a}_\text{n}$) - ($\text{b}_\text{n}$) is not convergent

Hint:

Algebra of Limits for convergent sequences \( (a_n) \to A \) and \( (b_n) \to B \):
- \( (a_n \pm b_n) \to A \pm B \).
- \( (a_n \cdot b_n) \to A \cdot B \).
- \( (a_n / b_n) \to A / B \) (provided \( B \neq 0 \)).

Answer 1

The Correct Option is A