system
Given the following post, respond as if you're commenting on Reddit:
human
Does the infinite series 1/1-1/2+1/3-1/4... converge?

I know the series 1 + 1/2 + 1/3 ... diverges, but if the sign changes every entry, does it still diverge?
gpt
The alternating harmonic series converges to log(2). You can prove its convergence using... the alternating series test. As for determining the exact value that's a matter of integrating the alternating geometric series term by term and using Abel's theorem.