 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/3/a/iii/solution

True. Rationalizing the square root gives, for

n \geq 1

0 \leq n^{2} + n - n = \frac{n}{n ^{2} + n + n} = \frac{1}{1 + 1/ n + 1} \leq \frac{1}{2} .

The uniform bound is exactly the assertion

O (1)

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