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The Root Test

Given the series $\displaystyle \sum_{n=0}^{\infty} a_n$, suppose that

\begin{displaymath}\lim_{n \rightarrow \infty} \sqrt[n]{\vert a_n\vert}=\rho \end{displaymath}

exists, then the series:
  1. Converges absolutely if $\rho<1$
  2. Diverges of $\rho>1$


Dina J. Solitro-Rassias
2017-11-09