## University Calculus: Early Transcendentals (3rd Edition)

Since, we have: $\int_1^\infty\sec h x dx=2\lim\limits_{a \to \infty} \int_1^a\frac{e^x}{1+(e^x)^2} dx$ or, $=2 [\lim\limits_{a \to \infty} [tan^{-1}(e^x)]|_{1}^{a}$ or, $=2 \lim\limits_{a \to \infty}(\tan^{-1} e^a-tan^{-1} e)$ or, $=\pi-2 tan^{-1} e$ or, $\approx 0.71$ Hence, the series is Convergent