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Notation: Tending to Infinity

publish date: 2026/05/23 22:07:20.701096 UTC

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Which of the following is the correct notation for "\(-n^2\) tends to \(-\infty\) as \(n\) tends to \(\infty\)"?

\(-n^2 = -\infty\) as \(n = \infty\)

\(-n^2 \to -\infty\) as \(n \to \infty\)

\(\lim -n^2 = 0\)

\(-n^2 < -\infty\) for large \(n\)

Correct Answer

\(-n^2 \to -\infty\) as \(n \to \infty\)

Explanation

The arrow notation \(-n^2 \to -\infty\) as \(n \to \infty\) correctly expresses that \(-n^2\) tends to (approaches) \(-\infty\) as \(n\) grows without bound. Writing \(-n^2 = -\infty\) is wrong because \(\infty\) is not a number — no quantity can equal infinity. The arrow \(\to\) expresses a process, not an equation.

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

Quizzes you can take where this question appears

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