Use the integral test, if applicable, to determine whether the series $\sum_{n=1}^{\infty} \frac{n+2}{n^{2}+n}$ converges or diverges.
A)It converges.
B)It diverges.
C)The integral test does not apply.

Question

Quizplus · Accepted Answer

The function $ f(x) = \frac{x+2}{x^2+x} $ is positive, continuous, and decreasing for $ x \geq 1 $. The integral $\int_{1}^{\infty} \frac{x+2}{x^2+x} \, dx$ diverges, indicating that the series diverges by the integral test.

Use the Integral Test, If Applicable, to Determine Whether the Series