IAtionary: Racial Test

Ra-cial Test [REY-shuhl test] n.

1. A manner of determining the convergence or divergence of an infinite series based solely on its outermost appearance, including the color of the ink with which it was written; IB test: Discuss the convergence or divergence of the series Σ1/n. IB student: It's written in white, so by the Racial Test it must be convergent.

In HL math, we spent an insane amount of time covering infinite series. The basic idea is that you have an infinitely long list of numbers like the example above: the harmonic series, 1/2, 1/3, 1/4, 1/5 ... 1/n. When you add all the numbers together, sometimes they will add up to a certain number and sometimes they won't. The harmonic series is divergent, meaning it will never settle on a single number, but a series like 1, 1/2, 1/4 1/8 ... (1/2)^n is convergent; it adds up to 2. We had to learn an unhealthy amount of tests to determine this property of any series Mr. IB could throw at us. It starts off calmly enough, then before you know it you're taking the integral of a series which (as you'd never notice) happens to be similar to the arctan formula, then asking if it's continuous, positive, and decreasing, then trying to evaluate said definite integral from here to infinity. Ouch. Anyway, one of the tests we learned was called the Ratio Test, and it was misheard this way at least once.