Maeckes logo

<    1      2      3      4      5      6      7      8      9     10     11    >


Binomium

The binomium of Newton (bi means the 2 variables a and b) is the formula

(a + b)n = an + n a− 1b + ½ n (n − 1) an −2b2  + ···

where n is a natural number.

 


Explanation

We write the binomium and find








It contains a clear regularity. Each term has the general form

Coefficient × an−r br

where

n = Power of the binomium
r = Number of the term

The development of the binomial coefficients follows Pascal's triangle.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1

A number is the sum of the number on the left and the right, just above it. In the rows these numbers increase at first, and decrease accordingly afterwards. There is of course a formula for that.

 


Deutsch   Español   Français   Nederlands