Exercise 1.1 Show that the sequence {a_n} defined by (1.1) is strictly increasing in n and that {b_n} defined by (1.2) is strictly decreasing. Hint: Use the inequalities (1 − x)ⁿ > 1 − nx, 0 < x < 1, and (1 + x)ⁿ > 1 + nx, x > 0, for n ≥ 2.