[0F1]If the ratio test [21C] can be applied, we have seen in the demonstration that, for a \(L{\lt}1\), there is a \(N\) for which \(|a_ n|≤ L^{n-N}a_ N\) for every \(n≥ N\), and therefore \(\limsup _{n→∞}\sqrt[n]{|a_ n|}≤ L {\lt}1\), that is the root test [21D] holds.
