MA 1971 Bridge to Higher Mathematics
Quiz 4
Show all work needed to reach your answers.
Consider the continued root
r
5 + q
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).
