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2016Fall-MATH243-03-Liu.J00770722.HW_Sec_9.1-9.2

2016Fall-MATH243-03-Liu.J00770722.HW_Sec_9.1-9.2 - Garry...

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Garry Geslin 2016Fall-MATH243-03-Liu Assignment HW Sec 9.1-9.2 due 08/31/2016 at 11:59pm CDT 1. (1 point) Suppose a 1 = 1 2 - 1 2 , a 2 = 2 3 - 1 3 , a 3 = 3 4 - 1 4 , a 4 = 4 5 - 1 5 , a 5 = 5 6 - 1 6 . a) Find an explicit formula for a n : . b) Determine whether the sequence is convergent or diver- gent: . (Enter ”convergent” or ”divergent” as appropriate.) c) If it converges, find lim n a n = . Answer(s) submitted: n/((1+n)-(1/(1+n))) convergent 1 (correct) 2. (1 point) Sequences: A sequence is of the form a 1 , a 2 , a 3 , a 4 ,... where the a n are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways: By listing , and appealing (via the three dots) to your intuition. Suppose the sequence is 1 2 , 2 5 , 3 10 , 4 17 , 5 26 , 6 37 ,... Then the n -th term is a n = . Explicitly. For example, suppose a n = n n . Then a 1 = , a 2 = , and a 3 = . Recursively. For example, the Fibonacci Sequence is defined by a 1 = a 2 = 1 , a n + 1 = a n + a n - 1 , n = 2 , 3 , 4 , ....
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