Question

If (sn) is a monotone sequence, then the sequence either ______, or _______ to +/- infinity.

A. Converges, diverges
B. Oscillates, stabilizes
C. Increases, decreases
D. Approaches, avoids

Answer 1

If (sn) is a monotone sequence, then the sequence either converges, or diverges to +/- infinity.

Step-by-step explanation:

If (sn) is a monotone sequence, then the sequence either converges, or diverges to +/- infinity.

In mathematics, a sequence is called monotone if it either always increases or always decreases. A sequence that increases or decreases without bound is said to diverge. On the other hand, a sequence that approaches a specific value is said to converge.

For example, the sequence (1, 2, 3, 4, ...) is a monotone sequence that increases and diverges to infinity, while the sequence (10, 9, 8, 7, ...) is a monotone sequence that decreases and diverges to negative infinity.