 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/19/b/i/solution

y_{*} = 2 + y_{*}

y_{*} \geq 0

. Squaring gives

(y_{*} - 2) (y_{*} + 1) = 0

, so the negative algebraic root is inadmissible. Hence

y_{*} = 2.

Starting at

y_{0} = 2

produces the constant sequence

2, 2, \dots

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