let ∑n = 1∞an be a series with nonzero terms. let ρ=limn→∞|an + 1an|. according to the ratio test, if 0≤ρ<1…

let ∑n = 1∞an be a series with nonzero terms. let ρ=limn→∞|an + 1an|. according to the ratio test, if 0≤ρ<1, then ∑n = 1∞an converges absolutely. ∑n = 1∞an diverges. ∑n = 1∞an converges conditionally. the test does not provide any information.

let ∑n = 1∞an be a series with nonzero terms. let ρ=limn→∞|an + 1an|. according to the ratio test, if 0≤ρ<1, then ∑n = 1∞an converges absolutely. ∑n = 1∞an diverges. ∑n = 1∞an converges conditionally. the test does not provide any information.

Answer

Explanation:

Step1: Recall Ratio - Test rule

The Ratio - Test states that for a series $\sum_{n = 1}^{\infty}a_n$ with $a_n\neq0$ and $\rho=\lim_{n\rightarrow\infty}\left|\frac{a_{n + 1}}{a_n}\right|$, if $0\leq\rho<1$, the series $\sum_{n = 1}^{\infty}a_n$ converges absolutely.

Answer:

$\sum_{n = 1}^{\infty}a_n$ converges absolutely.