Question

Improper Integrals: Determine whether the following improper integrals converge or diverge.

${\int }_1^{\infty }\frac{1}{x}dx.$

Short answer

It is the divergent series.

Step-by-step solution

Step 1. Given Information.

$Givenaseries:{\int }_1^{\infty }\frac{1}{x}dx.$

Step 2. Solving the integral.

$$\begin{gathered} {\int }_1^{\infty }\frac{1}{x}dx={\left[\ln x\right]}_1^{\infty }=\left[\ln \infty -\ln 1\right] \\ =\infty -0=\infty . \\ Therefore,theseriesisadivergentseries. \end{gathered}$$