Editing Root test (section)

{{Short description|Criterion for the convergence of an infinite series}}
{{Calculus |Series}}

In [[mathematics]], the '''root test''' is a criterion for the [[Convergent series|convergence]] (a [[convergence test]]) of an [[infinite series]].  It depends on the quantity
:<math>\limsup_{n\rightarrow\infty}\sqrt[n]{|a_n|},</math>
where <math>a_n</math> are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one.  It is particularly useful in connection with [[power series]].