## Series Convergence Analysis ### Problem Statement Evaluate the convergence or divergence of the series using the Integral Test: \[ \sum_{k=1}^{\infty} \frac{1}{k^{0.8}} \] ### Integral Test Use the Integral Test to determine whether the series converges or diverges. ### Options Select the correct answer: - ○ The series converges since the value of the integral is \(\frac{1}{0.2}\). - ○ The series diverges since the integral approaches \(\infty\). - ○ The series diverges since the integral approaches \(-\infty\). - ○ The series converges since the value of the integral is 0. ### Explanation To apply the Integral Test, consider the integral: \[ \int_{1}^{\infty} \frac{1}{x^{0.8}} \, dx \] Determine whether the result of this integral is finite or infinite to decide the behavior of the series.