An elegant result about sum of powers
February 5th, 2010
Here it is. It is highly non-trivial that the left hand side, involving sum of powers of integers, yields something like e. Elegant isn’t it. To prove it you need Euler-Maclaurin formula. It is said to be one of the indispensable tools in any mathematitian’s bag of tricks but not taught in any undergraduate course - regardless of its elementary nature, nothing more advanced than calculus. The proof can be found here