Final answer:
The integral test determines the convergence of an infinite series by integrating its terms. For a series to converge, the integral must be finite, and the terms must approach zero. Hence, the correct answer is that the series converges and the terms have limit 0.
Step-by-step explanation:
The integral test in mathematics is a method used to determine the convergence or divergence of an infinite series. The test states that if the terms of an infinite series are positive, continuous, and decreasing, and if integrating the function from 1 to infinity gives a finite value, then the series converges. However, for the series to converge, it's not enough that the terms of the series approach zero; the integral of these terms must also converge. If the integral diverges, then the series diverges as well.
Given this information, the correct answer is that the integral test can be used to conclude that Option A: The series converges, and the terms of the series have limit 0. Notably, for a series to converge, it's a necessary condition that the terms approach zero as the index goes to infinity, but it is not a sufficient condition on its own; the integral test must also confirm that the respective integral of the function that defines the series terms converges.