Use the nth-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive.
-$$\sum _ { n = 1 } ^ { \infty } \frac { n } { n + 6 }$$
A) diverges
B) converges, $\frac { 1 } { 6 }$
C) converges, 6
D) inconclusive

Question

Quizplus · Accepted Answer

Using the nth-Term Test for divergence, we take the limit as n approaches infinity of the nth term:
$$\lim_{n \to \infty} \frac{n}{n+6} = 1$$
Since the limit is not zero, the series diverges.

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