Always check the nth term first because if it doesn't converge to zero, you're done — the alternating series and the positive series will both diverge. Note that the nth term test of divergence applies to alternating series as well as positive series. ... Thus, the alternating series is conditionally convergent.

Can you use alternating series test to prove divergence?

No, it does not establish the divergence of an alternating series unless it fails the test by violating the condition limn→∞bn=0 , which is essentially the Divergence Test; therefore, it established the divergence in this case.

Can alternating series be absolutely convergent?

The notion that alternating the signs of the terms in a series can make a series converge leads us to the following definitions. A series ∞∑n=1an converges absolutely if ∞∑n=1|an| converges.