List of top Statistics Questions on sequences

Let \( \{a_n\} \) and \( \{b_n\} \) be sequences of real numbers such that \( \{a_n\} \) is increasing and \( \{b_n\} \) is decreasing. Under which of the following conditions, the sequence \( \{a_n + b_n\} \) is always convergent?
Let \( u_n = \frac{(4 - n)}{n} \), \( n \in \mathbb{N} \), and let \( l = \lim_{n \to \infty} u_n \).
Which of the following statements is TRUE?