Is Alternating Series Convergent?

This series is called the alternating harmonic series. This is a convergence-only test. In order to show a series diverges, you must use another test. ... If the terms do not converge to zero, you are finished.

Are alternating sequences convergent?

A sequence whose terms alternate in sign is called an alternating sequence, and such a sequence converges if two simple conditions hold: 1. Its terms decrease in magnitude: so we have . 2.

Can alternating series be conditionally convergent?

B. If the positive term series diverges, use the alternating series test to determine if the alternating series converges. If this series converges, then the given series converges conditionally. If the alternating series diverges, then the given series diverges.