12 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 ? k=1 b) Let {b} be a sequence with b, E {0, 1, 2,...,9}. Let In k=1 nondecreasing and bounded above by 1. Note: This shows that {r} converges and that if = lim rn, then 3 [0, 1]. 11-00 c) Let a [0, 1]. Define a = max{k {0, 1, 2,...,9}