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