Being no and P two natural numbers we call binomial coefficient class Pnumber no, the number , which we indicate by (reads: no about P). We can write:
The binomial coefficient is also called binomial number. By analogy with fractions, we say that no it's yours numerator and P, O denominator. We can write:
It is also immediate that for any no natural we have:
Examples:
Binomial Coefficient Properties
1ª)
If n, p, k and p + k = n then |
Binomial coefficients like these, which have the same numerator and the sum of the denominators equal to the numerator, are called complementary. Examples:
2ª)
If n, p, k and p p-1 0 then |
This equality is known as Stifel interface (Michael Stifel, German mathematician, 1487 - 1567). Examples:
Next: Pascal Triangle