EDB — 219

[219] Let $𝛼=\underset{n\to \infty }{lim sup}\sqrt[n]{|a_n|}$ then

• if $𝛼<1$ the series ${\sum }_{n=1}^{\infty }{a}_n$ converges absolutely;

• if $𝛼=1$ nothing can be concluded;

• if $𝛼>1$ the series ${\sum }_{n=1}^{\infty }{a}_n$ does not converge, and also ${\sum }_{n=1}^{\infty }|a_n|$ diverges.