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MA 1971 Bridge to Higher Mathematics Name:
Quiz 4 D Term,
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Consider the continued root
r
5 + 5 + 5 + …
1. Which sequence is equivalent to this continued root?
2.Call this sequence {an} = {a1,a2,a3,…} (just to give it and its terms a name). Please write down the recurrence formula giving an+1 in terms of an.
3.This sequence can be shown to be increasing, so to guarantee convergence, please use the recurrence formula to show the sequence is bounded above. Hint: Induction.
4.Please compute the value of this continued root (the limit of the sequence).
