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Example

• [1/i+1]_i is strictly monotonically decreasing:

  [1/i+1]_i = [1, 1/2, 1/3, 1/4, ...]

• [i div 2]_i is monotonically increasing:

  [i div 2]_i = [0, 0, 1, 1, 2, 2, ...]

• [(-1)ⁱ]_i is neither monotonically increasing nor decreasing:

  [(-1)ⁱ]_i = [1, -1, 1, -1, ...]