Question: Problem 3. A sequence {on} is given by the recurrence relation 01 = 2, On |1 = 5 (an + 6), VnEN. (i) By mathematical

Problem 3. A sequence {on} is given by the recurrence relation 01 = 2, On |1 = 5 (an + 6), VnEN. (i) By mathematical induction, show that { an } is nondecreasing and bounded above by 6. Deduce that {a, } is a convergent sequence. (zi) Calculate lim an. n > | 00 00 Problem 4. Determine whether the series converges or di- 73 + 1 1=1 verges. Show all your work (and state what test you use)

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