Root Test

Definition

Suppose $\sum _{n=1}^{\infty }{a}_n$ is a power series, and let $M:=\underset{n\to \infty }{\mathrm{limsup}}\sqrt[n]{|a_n|}$ If $M<1$, then $\sum _{n=1}^{\infty }{a}_n$ converges absolutely If $M>1$, then $\sum _{n=1}^{\infty }{a}_n$ diverges