Question

Test the series below for convergence using the Root Test. sum_{n=1}^{infty} (frac{4n + 4}{3n + 5})^n The limit of the root test simplifies to lim_{n o infty} |f(n)| where f(n) = The limit is: (enter oo for infinity if needed) Based on this, the series Diverges Converges

          Test the series below for convergence using the Root Test.
sum_{n=1}^{infty} (frac{4n + 4}{3n + 5})^n

The limit of the root test simplifies to lim_{n 	o infty} |f(n)| where

f(n) = 

The limit is: 
(enter oo for infinity if needed)

Based on this, the series

Diverges
Converges

$Test the series below for convergence using the Root Test. sumn=1^infty (frac4n + 43n + 5)^n The limit of the root test simplifies to limn o infty |f(n)| where f(n) = The limit is: (enter oo for infinity if needed) Based on this, the series Diverges Converges$

Added by Rachel B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Brent Burkett

Step 1

It seems there is a formatting issue in the question, but I assume the series is: $$\sum_{n=1}^{\infty} (4n + 4)^{3n + 5}$$ Now, we will apply the Root Test. We need to find the limit: $$\lim_{n \to \infty} \sqrt[n]{|(4n + 4)^{3n + 5}|}$$ To simplify this Show more…

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Test the series below for convergence using the Root Test. sum_{n=1}^{infty} (frac{4n + 4}{3n + 5})^n The limit of the root test simplifies to lim_{n o infty} |f(n)| where f(n) = The limit is: (enter oo for infinity if needed) Based on this, the series Diverges Converges