Determine convergence or divergence of the alternating series.
-$$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 5 n ^ { 3 } + 8 }$$
A) Diverges
B) Converges

Question

Quizplus · Accepted Answer

We can use the Alternating Series Test to determine the convergence of this series. First, note that the terms of the series are decreasing in absolute value because the denominator grows faster than the numerator. 
Also, $\lim_{n	o\infty}\dfrac{1}{5n^3+8}=0$ since the denominator grows much faster than the numerator and eventually dominates it. 
Therefore, by the Alternating Series Test, the series converges.

Determine Convergence or Divergence of the Alternating Series ∑n=1∞(−1)n5n3+8\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 5 n ^ { 3 } + 8 }n=1∑∞​5n3+8(−1)n​

Determine Convergence or Divergence of the Alternating Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 5 n ^ { 3 } + 8 }$