Use the Limit Comparison Test to determine the convergence or divergence of the series .
A)The series converges.
B)The series diverges.

Question

Use the Limit Comparison Test to determine the convergence or divergence of the series  . ​
A)The series converges. 
B)The series diverges.

Quizplus · Accepted Answer

We can use the Limit Comparison Test with the series 1/n.

Taking the limit as n approaches infinity of (11e^(n))/n, we get:

lim (n → ∞)  (11e^(n))/n = ∞

Taking the limit as n approaches infinity of 1/n, we get:

lim (n → ∞)  1/n = 0

Since the limit of the ratio of these two series is infinity, we can conclude that the series 11e^(n) is larger than the divergent harmonic series, and thus diverges.

However, the series 1/n converges by the p-series test with p=1.

Therefore, using the Limit Comparison Test, we can say that the series 11e^(n) and 1/n have the same convergence behavior. Since 1/n converges, the series 11e^(n) also converges.

Thus, the correct choice is A.

Use the Limit Comparison Test to Determine the Convergence or Divergence