Behaviour of f(n) = n² as n → ∞

It can be made as large as we please — it tends to +∞

Explanation

For \(f(n) = n^2\): as \(n\) increases, \(n^2\) exceeds any fixed bound \(K\) (simply take \(n > \sqrt{K}\)). We write \(n^2 \to +\infty\) as \(n \to \infty\). This is the standard notation for a function that grows without bound. In contrast, \(f(n) = -n^2 \to -\infty\) as \(n \to \infty\).