Let $\sum {u_n}$ be a series of positive terms and let $\begin{array}{*{20}{c}} {{\rm{lim}}u_n^{1/n}}\ {n \to \infty } \end{array} = l$, then, which among the following does not express the condition for the Cauchy’s nth root test?

Question

Let $\sum {u_n}$ be a series of positive terms and let $\begin{array}{*{20}{c}} {{\rm{lim}}u_n^{1/n}}\ {n \to \infty } \end{array} = l$, then, which among the following does not express the condition for the Cauchy’s nth root test?

TuteeHUB · Accepted Answer

If l = 1, the test fails and the series may either converge or diverge

TuteeHUB · Answer

If l > 1, ∑un diverges

TuteeHUB · Answer

If l < 1, ∑un converges

TuteeHUB · Answer

If l = 0, the series neither converges nor diverges

1.	Let \(\sum {u_n}\) be a series of positive terms and let \(\begin{array}{*{20}{c}} {{\rm{lim}}u_n^{1/n}}\\ {n \to \infty } \end{array} = l\), then, which among the following does not express the condition for the Cauchy’s nth root test?
A.	If l > 1, ∑un diverges
B.	If l < 1, ∑un converges
C.	If l = 0, the series neither converges nor diverges
D.	If l = 1, the test fails and the series may either converge or diverge
Answer» D. If l = 1, the test fails and the series may either converge or diverge

Let \(\sum {u_n}\) be a series of positive terms and let \(\begin{array}{*{20}{c}} {{\rm{lim}}u_n^{1/n}}\\ {n \to \infty } \end{array} = l\), then, which among the following does not express the condition for the Cauchy’s nth root test?

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