16) Decimal Expansion [16 Marks, 4 for each part] Note: In this question we are going to see how to use the MCT to build a decimal expansion for every real number in [0, 1]. a) What is > b) Let {b, } be a sequence with by 6 {0, 1, 2, ...,9 ). Let mm = _ . Show that {r, } is K=1 nondecreasing and bounded above by 1. Note: This shows that {r, } converges and that if 8 = lim mm, then B e [0, 1]. n-+co c) Let a E [0, 1). Define a, = max {ke {0, 1, 2, ...,9} | & co). Then let s] = #. Observe that 0