Pascal’s triangle relations and the binomial theorem (HSC SSCE Mathematics Extension 1): Flashcards

A triangle where each number is the sum of the two above.

It expands powers of sums using coefficients.

Begin with a single '1' at the top.

The total is $2^n$.

It's written as inom{n}{r} in expansions.

It expands to $a^2 + 2ab + b^2$.

$(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$.

It finds specific coefficients in expansions.

Use inom{5}{3} = 10 for the term.

It's useful in combinatorial maths and probability.