There is no single unique "value" obtainable for a nonconvergent series through rearranging, regrouping, adding, etc. nonconvergent series. If you check out comments for the Numberphile video, you can find several different values produced for the same series, and although many of them are done incorrectly there are still several cases that correctly perform operations that would be allowed for convergent series. Once you have several different values all "equal" to the same thing, you can in principle derive all sorts of nonsense including 1=0.
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