Does the human calculator stuff really work?

jim1174
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There are a lot of books and videos that can teach you how to do math in your head. does any of it really work.
Is there a certain book or video that you would recomend
 
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It is possible to do math in your head, therefore, yes. Doing it fast and with complicated operations requires a lot of practice and various tricks. I don't know specific books for that.
 
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I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
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