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

Question

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

Quizplus · Accepted Answer

We apply the Ratio Test for convergence:
$\lim_{n 	o \infty}\left|\frac{a_{n+1}}{a_n}ight| = \lim_{n 	o \infty}\left|\frac{11e^{(a+1)^5}}{11e^{a^5}}ight| = \lim_{n 	o \infty}\left|e^{(a+1)^5-a^5}ight| = \infty$
Since the limit is infinity, the series diverges. Therefore, the answer is (C) diverges.

Use the Ratio Test to Determine the Convergence or Divergence