Clik here to view.
The smart way to do the binomial expansion (Part 1)
Ah, the binomial expansion. The scourge of my A-level: the sum that was always wider than the paper, and always had one more minus sign than I’d allowed for. A crazy, pointless exercise in arithmetic,...
View ArticleThe smart way to do the binomial expansion (Part II)
This is a follow-up to Monday’s post about the smart way to do the binomial expansion. In this one, we’re going to look at how to do C4 binomial expansions – ones with crazy powers like $-3$ or...
View ArticleSecrets of the Mathematical Ninja: Pascal’s Triangle
You’ve seen Pascal’s triangle before: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 You get the number in each row by adding its two ‘parents’ – for instance, each 10 in the row that starts with 1 then 5...
View ArticleWhy I don’t buy that $1 + 2 + 3 + … = -\frac{1}{12}$
Thanks to Robert Anderson for the question. I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once...
View ArticleBlazing through the Binomial Expansion
“Where’s the Mathematical Ninja?” asked the student. “He’s… unavoidably detained,” I said. In fact, he was playing Candy Crush Saga. But sh. “What can I help you with today?” “Well, you know the...
View ArticleWhy the Maclaurin series gives you Pascal’s Triangle
The Mathematical Ninja, some time ago, pointed out a curiosity about Pascal’s Triangle and the Maclaurin1 (or Taylor2 ) series of a product: $\diffn{n}{(uv)}{x} = uv^{(n)} + n u’v^{(n-1)} +...
View ArticleAsk Uncle Colin: A logarithmic coincidence?
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to...
View ArticleAsk Uncle Colin: Is my friend crazy?
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to...
View ArticleA STEP expansion
A STEP question (1999 STEP II, Q4) asks: By considering the expansions in powers of $x$ of both sides of the identity $(1+x)^n (1+x)^n \equiv (1+x)^{2n}$ show that: $\sum_{s=0}^{n} \left( \nCr{n}{s}...
View ArticleWhy $\phi^n$ is nearly an integer
This article is one of those ‘half-finished thoughts’ put together late at night. Details are missing, and — in a spirit of collaboration — I’d be glad if you wanted to fill them in for me. The...
View ArticleThe Mathematical Ninja and the Nineteenths
“Look,” said the student, “we all know how this goes down. A nasty-looking fraction comes out of the sum, I reach for the calculator, you commit some act of exaggerated violence and tell me how you, o...
View ArticleAsk Uncle Colin: Why is it not 4?
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to...
View Article
