The series $\sum \frac{(-1)^{n+1}(n^2+4)^{1/3}}{(n^5+1)^{1/2}}$ converges based on the Alternating Series Test. The necessary conditions for convergence were confirmed: the terms $a_n = \frac{(n^2+4)^{1/3}}{(n^5+1)^{1/2}}$ are positive, the sequence is monotonically decreasing, and the limit of $a_n$ approaches 0 as $n$ approaches infinity. Therefore, the series satisfies all criteria for convergence.
PREREQUISITESStudents studying calculus, particularly those focusing on series and convergence tests, as well as educators teaching these concepts in mathematics courses.