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Just to clarify, I think Elizabeth Warren is a complete fraud here, because she claimed she had Cherokee ancestry and she claimed that her mother was recognized as Cherokee and suffered discrimination for it...which on the evidence is completely untrue. Warren is no more Cherokee than your average US non-Cherokee citizen, and there has been no evidence that she or her mother had any Cherokee ancestor much less one that was recent enough for her story to be plausible. My issue here is purely with how to do a math problem.

Wrong! There was no exact generation reported for her suspected “Indian” DNA.

I did not dispute that there is no exact generation reported, nor do vouch for the accuracy of the report, I merely ran the numbers. Nor do I vouch for the alleged ancestor in the report being native to North America rather than South America. I was only doing the math based on the reports claims. Based on the report at face value the math the range is 1/64th to 1/1024th.

It was a range of generations, and so the original “Indian” ancestor would be one of 992 possible persons or approximately a 0.1 percent chance that she is part Indian, assuming that her DNA from Mexico, Peru, and Colombia is actually Indian DNA.

Yes it was a range. However your math used generations outside of that range including fourth generation when the reported range was 6th to 10th and average of 8th. Moreover, summing the number of people in different generation as a denominator for DNA contribution of an individual is just an entirely incorrect approach to the problem. While all the ancestors in a particular generation with the same weight, ancestors in different generations have different weight. For example our parents each have a 1/2 contribution to our DNA by contrast our 10th generation ancestors each have a 1/1024th.