Yes, I'm talking about that same Gradi's Sequence. I don't think it can be used in the proof of the original video precisely because it is not a sum of all natural numbers. The two premise formulae, S1 and S2, upon which the "proof" in the original video is based, IMO, is the problem. The conclusion, or proof, is based on a faulty premise. Arbitrarily deciding to average the two results of the sequence to get 1/2 is flawed.
I also think S2 is flawed because there is no requirement that all natural numbers have to be added in sequence. If you took 2+3+127865+99+872...and never repeated a number and then applied his trick of shifting the numbers over with a different randomly ordered sequence, the result would be totally different and not result in the 1/4 solution.
I'm left with the obvious analogy of adding a whole bunch of peas and never getting to a final sum, much less one that is a negative fraction and not itself a natural number.
Agreed on all counts.
There are things you cannot do with zero and infinity because they break the rules of mathematics.