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

The Root Test states that if the limit as n approaches infinity of the nth root of the absolute value of the nth term is greater than 1, then the series diverges. In this case, we have:

lim (n→∞) (|11e^n|)^(1/n) = lim (n→∞) 11^(1/n) * e
= e > 1

Therefore, the series diverges.

Use the Root Test to Determine the Convergence or Divergence