Use the Root Test to determine the convergence or divergence of the series.
A) converges
B) diverges
C) Root Test inconclusive

Question

Use the Root Test to determine the convergence or divergence of the series. 
A) converges 
B) diverges 
C) Root Test inconclusive

Quizplus · Accepted Answer

Using the Root Test, we take the limit as n goes to infinity of the nth root of the absolute value of the terms:
lim(n -> ∞) (|11e^(aa595+6475n)/4^n|)^(1/n)

= lim(n -> ∞) (11e^(aa595+6475n)/4^n)^(1/n)

= lim(n -> ∞) (11^(1/n)*e^((aa595+6475n)/n)/4)

=lim(n -> ∞) e^(6475/4)

Since this limit is greater than 1, the series diverges by the Root Test. Therefore, the best choice is B) diverges.

Use the Root Test to Determine the Convergence or Divergence