Q32Section B (Section B)32 of 60

Convergence of the sum of an increasing and a decreasing sequence

Let $\{a_n\}_{n\ge1}$ and $\{b_n\}_{n\ge1}$ be sequences of real numbers such that $\{a_n\}_{n\ge1}$ is increasing and $\{b_n\}_{n\ge1}$ is decreasing. Under which of the following conditions, the sequence $\{a_n+b_n\}_{n\ge1}$ is always convergent?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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