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MATH08059 Proofs and Problem Solving 3. (a) (i) Prove by induction that _ MATH08059 3. Proofs and Problem Solving (a) (i) Prove by induction that

MATH08059 Proofs and Problem Solving 3. (a) (i) Prove by induction that _

MATH08059 3. Proofs and Problem Solving (a) (i) Prove by induction that E n I < 2 L for all n e N. (ii) Prove that the set S = {Ekt=l : n 1} is bounded. 4 [6 marks] [2 marks] (b) Find the least upper bound of each of the following sets, justifying your answer fully. (ii) B = {n 2 (iii) C = {Eli=12-k : n e N}. [12 marks]

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