EDB — 219

[219] Let \(𝛼=\limsup _{n→∞}\sqrt[n]{|a_ n|}\) then

• if \(𝛼{\lt}1\) the series \(∑_{n=1}^∞ a_ n\) converges absolutely;

• if \(𝛼=1\) nothing can be concluded;

• if \(𝛼{\gt}1\) the series \(∑_{n=1}^∞ a_ n\) does not converge, and also \(∑_{n=1}^∞ |a_ n|\) diverges.