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

Table of contents
- Solution 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)

in Big O notation.

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