Question: QUESTION 1 Question 1. Sequences (13 marks) (a) Prove that the following sequences converge and determine their limits. 3n3 - 2n2 +4n - 2 i.

QUESTION 1

Question 1. Sequences (13 marks) (a) Prove that the following sequences converge and determine their limits. 3n3 - 2n2 +4n - 2 i. an = 2n13 + 2n - 1 [2 marks] ii. by = n sin (n) n2 +1 [2 marks] 4n2 + cos() iii. CA = 12+ 2n +2 [2 marks] iv. dn = V2" + 3 + 5 [2 marks] Hint. By calculating d, for large n, you can guess the limit L. Then consider dividing d, by L. v. fn = (1+*)n-1 [2 marks] Note. Here k is any real number. (b) Turn the following infinite expression into a sequence and use the monotone bounded sequence theorem to determine its value. 1/21/2\\/2V/2 ... [3 marks]

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