Deep dive into DIVErgence test
00:00 Divergence test
4:42 Conditionally convergent
6:15 Back to divergence test
7:23 Solving the problem
We discuss the divergence test in detail, and talk about why it doesn’t help with the problem at hand. We also talk about conditionally convergent series, with the alternating harmonic series as an example. Then we move on to solving the problem using the limit comparison test.
Reid asked me why conditionally convergent series are called that, and the reason seems to be that they can be rearranged to converge to any number or to even diverge to either positive or negative infinity! (Is this math or is it magic?) So the convergence is conditional on the order of summation. Look up Riemann series theorem if you are interested to learn more.