Chapter 2, Exercise 56

The green points below show the sequence \(x_n = 1 + \frac{(-1)^n}{n}\). When you select a value for \(N\) on the slider, the point \(u_N\) is shown in blue and \(v_N\) is shown in orange. Move the slider to see how the sequences that define the limit infimum and limit supremum change. Does this agree with what you observed in answering the other parts of this exploration in the text?