 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability-resit/2/c/iii/solution

True. Rationalization gives, for

n \geq 1

4 n^{2} + n - 2 n = \frac{n}{4 n ^{2} + n + 2 n} = \frac{1}{4 + 1/ n + 2} .

This lies between zero and

1/4

, so it is

O (1)

in Big O notation. In fact it converges to

1/4

, rather than to zero. The rationalized form also avoids the catastrophic cancellation of subtracting two nearby large quantities.

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