Monthly Archives: May 2016

A method of evaluating a double integral that nobody taught you in school

Many times we are given integrals to evaluate. The standard way to evaluate is to find a series of transformations that will render the integral into something we know how to evaluate and then proceed. Examples of such transformations are substitutions, parts, replacement of an integrand with another integral, reversing order of integration, and so […]

Deceptively easy product

The problem is to evaluate $$\prod_{n=2}^{\infty} \left (1+\frac{(-1)^{n-1}}{a_n} \right ) $$ where $$a_n = n! \sum_{k=1}^{n-1} \frac{(-1)^{k-1}}{k!} $$ This is one of those cases where trying out a bunch of numbers really isn’t going to help all that much. The $a_n$ look kind of like $n!$, except off by some. Even so, I can find […]