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Consider the continued root
r
5 + 5 + 5 + …
1. (2 points) Which sequence is equivalent to this continued root?
2. (3 points) 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. (12 points) 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. (8 points) Please compute the value of this continued root (the limit of the sequence).