[tex] \boxed{ \int_{a}^{ + \infty }f(x)dx = \lim_{b \to + \infty } \int_{a}^{b}f(x)dx } \\ \\ \int_{1}^{ + \infty } \frac{1}{x {}^{2} } \: dx \: \to \: \lim_{b \to + \infty }\int_{1}^{ b} \frac{1}{x {}^{2} }dx \: \\ \\ \lim_{b \to + \infty }\int_{1}^{ b} x {}^{ - 2} \: dx \: \to \: \lim_{b \to + \infty } \left[ - \frac{1}{x} \right] _{1}^{ b} \\ \\ \lim_{b \to + \infty } \left[ - \frac{1}{b} + \frac{1}{1} \right] \: \to \: \lim_{b \to + \infty } \left[ - \frac{1}{b} + 1 \right] \\ \\ \lim_{b \to + \infty } \left[ - \cancel {\frac{1}{ \infty }}^{0} + \frac{1}{1} \right] \: \to \: \lim_{b \to + \infty }(1) = \boxed{ 1}[/tex]

A resposta é que ela converge pra 1