Compute the value of the following improper integral. If it converges, enter its value. Enter infinity if it diverges to $\infty$, and -infinity if it diverges to $-\infty$. Otherwise, enter diverges.

$\displaystyle \int_{1}^{\infty} \frac{3 \, dx}{x^2 + 1}$ =

Does the series $\displaystyle \sum_{n=1}^{\infty} \frac{3}{n^2 + 1}$ converge or diverge? ? converges diverges to +infinity diverges to -infinity diverges