consider the series ∑∞n = 1an. ∑n = 1∞an. let ρ = limn→∞n|an|. according to the root test, if ρ = 1, then ∑n…

consider the series ∑∞n = 1an. ∑n = 1∞an. let ρ = limn→∞n|an|. according to the root test, if ρ = 1, then ∑n = 1∞an converges absolutely. ∑n = 1∞an converges conditionally. ∑n = 1∞an diverges. the test does not provide any information.

consider the series ∑∞n = 1an. ∑n = 1∞an. let ρ = limn→∞n|an|. according to the root test, if ρ = 1, then ∑n = 1∞an converges absolutely. ∑n = 1∞an converges conditionally. ∑n = 1∞an diverges. the test does not provide any information.

Answer

Explanation:

Step1: Recall Root - Test rules

The Root - Test states that for the series $\sum_{n = 1}^{\infty}a_n$ with $\rho=\lim_{n\rightarrow\infty}\sqrt[n]{\vert a_n\vert}$, if $\rho<1$, the series converges absolutely; if $\rho > 1$, the series diverges; if $\rho=1$, the Root - Test is inconclusive.

Answer:

the test does not provide any information.