Use the nth-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive.
-$$\sum _ { n = 1 } ^ { \infty } \frac { n } { n + 2 }$$
A) inconclusive
B) converges, 2
C) converges, $\frac { 1 } { 2 }$
D) diverges

Question

Quizplus · Accepted Answer

The nth-Term Test for divergence states that if the limit of the nth term as n approaches infinity does not exist or is not zero, then the series diverges. 
In this case, we have: 
$$\lim_{n\to\infty}\frac{n}{n+2}=\lim_{n\to\infty}\frac{n/n}{n/n+2/n}=\lim_{n\to\infty}\frac{1}{1+2/n}=1\neq0$$
Therefore, the series diverges.

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