Question: 2. (a) Let p be a real number such that p>-1 and p0. Prove by induction that (1+p) > 1+mp for every integer #

2. (a) Let p be a real number such that p>-1 and

2. (a) Let p be a real number such that p>-1 and p0. Prove by induction that (1+p)" > 1+mp for every integer # 22. (15 marks) (b) Using your results in (a) above, show that the sequence an = (1+)" for all integers n21 is a monotone increasing sequence. 10 marks) EXAMINER: E. Djabang (c) i. Use the comparison test to test for convergence for Se 8 In a (x-3)4 72=== (7 marks) ii. Use the ratio criterion test to find the interval of absolute convergence of the power series Page 1 of 3 xn n.3n-1 YRARGU (8 marks)

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Answer a Induction Proof Base Case n 2 We need to show 1 p 1 p2 Since p 1 and p 0 both sides are positive Multiplying both sides by 2 we get 2 2p 2 p ... View full answer

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