Series Convergence Testing Cheat Sheet

The Series Convergence Testing Cheat Sheet is a document that provides a handy reference guide for determining the convergence or divergence of different types of series in mathematics. It helps individuals quickly identify the tests and criteria that can be used to evaluate the behavior of mathematical series.

FAQ

Q: What is series convergence testing?A: Series convergence testing is a method used to determine whether a series converges or diverges.

Q: What is a convergent series?A: A convergent series is a series that has a finite sum.

Q: What is a divergent series?A: A divergent series is a series that does not have a finite sum.

Q: What is the divergence test?A: The divergence test states that if the terms of a series do not approach zero, then the series must diverge.

Q: What is the integral test?A: The integral test is a convergence test that relates the convergence of a series to the convergence of an associated improper integral.

Q: What is the comparison test?A: The comparison test is a convergence test that compares the terms of a series to the terms of a known convergent or divergent series.

Q: What is the limit comparison test?A: The limit comparison test is a convergence test that compares the terms of a series to the terms of a known convergent or divergent series by taking the limit of the ratio of the terms.

Q: What is the ratio test?A: The ratio test is a convergence test that compares the absolute value of the terms of a series to the ratio of consecutive terms.

Q: What is the root test?A: The root test is a convergence test that compares the absolute value of the terms of a series to the limit of the nth root of the absolute value of the terms.

Q: What is the alternating series test?A: The alternating series test is a convergence test that applies to alternating series and states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.

Q: What is the absolute convergence test?A: The absolute convergence test states that if the absolute values of the terms of a series converge, then the series converges.

Q: What is the conditional convergence test?A: The conditional convergence test states that if a series converges, but the absolute values of the terms do not converge, then the series is conditionally convergent.