Question

Test the series below for convergence using the root test.\\ $\sum_{n=1}^{\infty} \left(\frac{8n}{5n+5}\right)^n$\\ The limit of the root test simplifies to $\lim_{n\to\infty} |f(n)|$ where\\ $f(n) = $\\ The limit is \\ Based on this, the series Select an answer

          Test the series below for convergence using the root test.\\
$\sum_{n=1}^{\infty} \left(\frac{8n}{5n+5}\right)^n$\\
The limit of the root test simplifies to $\lim_{n\to\infty} |f(n)|$ where\\
$f(n) = $\\
The limit is \\
Based on this, the series Select an answer

Test the series below for convergence using the root test.

∑n=1^∞((8n)/(5n+5))^n

The limit of the root test simplifies to limn→∞ |f(n)| where

f(n) =

The limit is

Based on this, the series Select an answer

Added by Thomas S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

05/16/2023

Step 1

Step 1: Apply the root test to the series ∑ (8n / (5n + 5)). Show more…

Show all steps

Thanks for your feedback!

Test the series below for convergence using the root test: ∑ (8n / (5n + 5)), n=1 The limit of the root test simplifies to lim (n→∞) |(8n / (5n + 5))|^(1/n) The limit is 8/5 Based on this, the series converges.