Use the nth-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive.
-$$\sum _ { n = 1 } ^ { \infty } \cos \frac { 8 } { n }$$
A) converges, 1
B) converges, 8
C) diverges
D) inconclusive

Question

Quizplus · Accepted Answer

The nth-Term Test for divergence states that if the limit of the nth term as n approaches infinity is not equal to zero, then the series diverges. In this case, the nth term is $\cos\frac{8}{n}$. As $n$ goes to infinity, $\frac{8}{n}$ goes to zero, so $\cos\frac{8}{n}$ approaches $\cos 0 = 1$. Since the limit of the nth term is not zero, the series diverges. Therefore, the answer is C.

Use the Nth-Term Test for Divergence to Show That the Series