Use the Integral Test to determine the convergence or divergence of the series. $$\sum _ { n = 1 } ^ { \infty } \frac { 2 } { 9 n + 2 }$$
A) diverges
B) Integral Test inconclusive
C) converges

Question

Quizplus · Accepted Answer

We use the Integral Test:
$$\int_{1}^{\infty} \frac{2}{9n+2} dn = \lim_{b 	o \infty} \left[\frac{2}{9} \ln|9n+2| ight]_{1}^{b} = \infty$$
Since the integral diverges, the series $\sum_{n=1}^{\infty} \frac{2}{9n+2}$ also diverges. Therefore, the answer is (A) diverges.

Use the Integral Test to Determine the Convergence or Divergence ∑n=1∞29n+2\sum _ { n = 1 } ^ { \infty } \frac { 2 } { 9 n + 2 }n=1∑∞​9n+22​

Use the Integral Test to Determine the Convergence or Divergence $\sum _ { n = 1 } ^ { \infty } \frac { 2 } { 9 n + 2 }$