# November, 2019

## Ask Uncle Colin: An Exponential Limit

Dear Uncle Colin, I need to work out the limit of $\frac{2^{3x} - 1}{3^{2x}-1}$ as $x \to 0$, and I don’t have any ideas at all. Do you? - Fractions Rotten, Exponents Generally Excellent Hi, FREGE, and thanks for your message! There are a couple of ways to approach this:

## A Harmonic Conundrum

This one came from user_1312 on reddit with a heading “This is a bit tricky… Enjoy!”. What else can we do but solve it? Let $m$ and $n$ be positive numbers such that $\frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{101}$. Prove that $m-n$ is a multiple

## Wrong, But Useful, Episode 73

In this month's episode of Wrong, But Useful, we talk to @AJMagicMessage, who is Andrew Jeffrey in real life, and one of the driving forces behind Maths Week England, which in 2019 is November 11th to 15th. Apologies for a few issues with feedback in this episode. Dave takes full

## Ask Uncle Colin: How many draws?

Dear Uncle Colin, I’m trying to figure out how many possible draws there are for the Champions’ League quarter-finals. There are eight teams involved, and let’s assume first leg home advantage doesn’t matter (so A vs B is the same as B vs A) and there’s no restriction on which

## Dictionary of Mathematical Eponymy: The Kovalevskaya Top

When I was about eight, my parents bought, as a Christmas gift for my brother and me, a “Jungle Gym”, plastic tubes and connectors that fit together to make whatever the imagination came up with, a sort of large-scale Meccano. My brother went out into the garden to build castles