> I was skeptical of their claim that (-1)^n converges to 1/2
I don't think the authors of the video ever claim that the sum 1-1+1-1+... converges. The partial sum S_n
(the sum of the first n elements of the series) is either 0 for n even or 1 for n odd, which means that the
partial sums do not have a limit and so the infinite sum 1-1+1-1+... does not converge.