Category Archives: Summability Methods

$\sum_{n=0}^\infty e^{nix}$ is Cesàro Summable

Posted on September 29, 2015 by Sung Lee

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 →

Posted in Summability Methods | 5 Comments

$1+2+3+4+\cdots=-\frac{1}{12}$?

Posted on August 27, 2014 by Sung Lee

No, folks! I am not drunk nor I am pot-headed. 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 →

Posted in Foundations of Mathematics, Summability Methods | 4 Comments