Use the integral test to determine whether the series converges.
-$$\sum _ { n = 1 } ^ { \infty } \frac { 3 n } { n ^ { 2 } + 4 }$$
A) converges
B) diverges

Question

Quizplus · Accepted Answer

The integral test involves comparing the series to an improper integral. The function $ f(x) = \frac{3x}{x^2 + 4} $ is positive, continuous, and decreasing for $ x \geq 1 $. The integral $\int_{1}^{\infty} \frac{3x}{x^2 + 4} \, dx$ diverges, indicating that the series also diverges.

Use the Integral Test to Determine Whether the Series Converges ∑n=1∞3nn2+4\sum _ { n = 1 } ^ { \infty } \frac { 3 n } { n ^ { 2 } + 4 }n=1∑∞​n2+43n​

Use the Integral Test to Determine Whether the Series Converges $\sum _ { n = 1 } ^ { \infty } \frac { 3 n } { n ^ { 2 } + 4 }$