Question

You can study the convergence of the series $\sum_{n=1}^{\infty} (-1)^n \left(\frac{8n}{8n+1}\right)^{n^2}$ by using the Root Test. First you calculate $\lim_{n \to \infty} \sqrt[n]{|a_n|} = \underline{\qquad\qquad}$ to finally conclude that the series is $\circ$ convergent $\circ$ divergent

          You can study the convergence of the series $\sum_{n=1}^{\infty} (-1)^n \left(\frac{8n}{8n+1}\right)^{n^2}$ by using the Root Test.
First you calculate $\lim_{n \to \infty} \sqrt[n]{|a_n|} = \underline{\qquad\qquad}$ to finally conclude that the series is
$\circ$ convergent
$\circ$ divergent

You can study the convergence of the series ∑n=1^∞ (-1)^n ((8n)/(8n+1))^n^2 by using the Root Test.
First you calculate limn →∞√(|an|) = to finally conclude that the series is
∘ convergent
∘ divergent

Added by Wendy M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/09/2023

Step 1

Step 1: Calculate the general term $a_{n}$ of the series: \[a_{n} = (-1)^{n}\left(\frac{8n}{8n+1}\right)^{n^{2}}\] Show more…

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You can study the convergence of the series sum_{n=1}^{infty} (-1)^{n}left(frac{8n}{8n+1} ight)^{n^{2}} by using the Root Test. First, you calculate lim_{n oinfty} sqrt[n]{|a_{n}|} to finally conclude that the series is convergent or divergent by using the Root Test. First, you calculate lim_{n oinfty} a_{n} to finally conclude that the series is convergent or divergent.