Math  /  Calculus

QuestionUse the Root Test to determine whether the series convergent or divergent. n=2(7nn+1)3n\sum_{n=2}^{\infty}\left(\frac{-7 n}{n+1}\right)^{3 n}
Identify ana_{n}. \square
Evaluate the following limit. limnann\lim _{n \rightarrow \infty} \sqrt[n]{\left|a_{n}\right|} \square
Since limnann\lim _{n \rightarrow \infty} \sqrt[n]{\left|a_{n}\right|} \square ? 1, \square -Select--

Studdy Solution
Compare the limit to 1 and determine convergence or divergence:
Since limnann=343\lim_{n \to \infty} \sqrt[n]{|a_n|} = 343, which is greater than 1, the series diverges by the Root Test.
The series is divergent\boxed{\text{divergent}}.

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