This concept covers the Integral Test for series convergence: for a series whose terms are given by a positive, decreasing function evaluated at integers, the series converges if and only if the corresponding improper integral of that function over the same unbounded interval converges, allowing convergence questions about series with no closed-form partial sums to be resolved via improper integral evaluation. It relies on the formal hypotheses of the test (the associated function must be positive and decreasing on the interval in question) and on techniques for evaluating improper integrals, including substitution and limit evaluation at infinity. This belongs to single-variable calculus, within the theory of infinite series convergence tests, connecting series behavior to integral (and thus differential/antiderivative) calculus.
This concept covers the Integral Test for series convergence: for a series whose terms are given by a positive, decreasing function evaluated at integers, the series converges if and only if the corr…