A monotone sequence is a sequence of real numbers that either increases or decreases in absolute value for all natural numbers. In simpler terms, the sequence e...
A monotone sequence is a sequence of real numbers that either increases or decreases in absolute value for all natural numbers. In simpler terms, the sequence either goes up or down by the same amount for every step.
For example, the sequence 1, 3, 5, 7, 9 is a monotone sequence. Each term is the next number in the sequence, increasing by 2.
The first step to determining if a sequence is monotone is to examine the difference between consecutive terms. If the difference is constant and positive, the sequence is increasing; if the difference is constant and negative, the sequence is decreasing.
Furthermore, a monotone sequence is either convergent or divergent. A sequence is convergent if the limit of the sequence exists, while a sequence is divergent if the limit of the sequence is infinite