[Solved] MA1971 Quiz 4

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 {a_n} = {a₁,a₂,a₃,} (just to give it and its terms a name). Please write down the recurrence formula giving a_n+1 in terms of a_n.
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).