Root test

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In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity

${\displaystyle \limsup _{n\rightarrow \infty }{\sqrt[{n}]{|a_{n}|}},}$

where ${\displaystyle a_{n}}$ 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.