A sequence is called monotonic if one of the following properties hold: In the sequence {x_n}_n≥1, it is increasing if and only if x_n <>_n + ₁ for any n ≥ 1, or it is decreasing if and only if x_n > x_n + ₁ for any n ≥ 1.

For example, in order to check that the sequence {2ⁿ}_n≥1 is increasing: Let n ≥ 1; that gives 2ⁿ⁺¹ = 2ⁿ 2. Because 2 is greater than 1, which means that 1 × 2ⁿ < 2="" ×="">ⁿ; thus 2ⁿ <>^{n + 1}, which shows the sequence is increasing.