volume_mute
Behaviour of f(n) = 1/n as n → ∞
publish date: 2026/05/23 22:07:19.888241 UTC
volume_mute
The table below shows the values of \(f(n) = 1/n\) as \(n\) grows.
| x | f(x) = 1/x |
|---|---|
| 10 | 0.1 |
| 100 | 0.01 |
| 1000 | 0.001 |
| 10000 | 0.0001 |
What does \(f(n) = 1/n\) approach as \(n\) tends to infinity?
Correct Answer
It approaches 0, but never actually equals 0
Explanation
As \(n\) increases without bound, \(1/n\) gets closer and closer to 0 — but never equals 0 for any finite \(n\), since \(1 \ne 0\). It is correct to say \(1/n\) tends to 0 as \(n \to \infty\), but wrong to say \(1/n = 0\) when \(n = \infty\) (because \(\infty\) is not a number). This distinction is foundational for the concept of a limit.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012