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$\sum_{n=0}^\infty e^{nix}$ is Cesàro Summable
Back when I was a Ph.D. student, a friend of mine (he was a Ph.D. student in physics studying laser optics) asked me if the series $\sum_{n=0}^\infty e^{nix}$ converges. I vaguely remember that his advisor needed to have a finite … Continue reading
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$1+2+3+4+\cdots=\frac{1}{12}$?
No, folks! I am not drunk nor I am potheaded. Yet, I am about to discuss the crazy identity $$1+2+3+4+\cdots=\frac{1}{12}.$$ No, I am not joking either. This is actually pretty serious mathematics and is also pretty serious stuff even to … Continue reading