Determine convergence or divergence of the alternating series.
-$$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { n ^ { 3 / 4 } }$$
A) Diverges
B) Converges

Question

Quizplus · Accepted Answer

We can use the Alternating Series Test, which states that if a series has alternating signs and the absolute values of the terms decrease and approach zero, then the series converges. In this case, $\frac{1}{n^{3/4}}$ is decreasing and approaching zero as $n$ approaches infinity. Therefore, the series converges.

Determine Convergence or Divergence of the Alternating Series ∑n=1∞(−1)nn3/4\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { n ^ { 3 / 4 } }n=1∑∞​n3/4(−1)n​

Determine Convergence or Divergence of the Alternating Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { n ^ { 3 / 4 } }$