Applying Series Convergence Tests

Question

Which of the following statements about the series $$\displaystyle\sum_{n=1}^{\infty} \frac{n+2}{n^2+n}$$ is true?

Accepted Answer

The series can be shown to diverge by direct comparison with $$\displaystyle\sum_{n=1}^{\infty} \frac{1}{n}$$.

Answer

The series can be shown to converge by limit comparison with $$\displaystyle\sum_{n=1}^{\infty} \frac{1}{n^2}$$.

Answer

The series can be shown to converge by the ratio test.

Answer

The series can be shown to converge by the alternating series test.

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