Learning Ashram

The Binomia Formula & Binomial Coefficients

FACTORIAL n
If n = 1,2,3, . . . factorial n or n factorial is defined as
n! = 1-2-3 n
We also define zero factorial as
0! = 1
BINOMIAL FORMULA FOR POSITIVE INTEGER n
If n = 1,2,3, . .. then


This is called Binomial Formula. It can be extened to other vaues of n and then is an infinite series.
BINOMIAL COEFFICIENTS

where the coefficients, called binomial coefficients, are given by
PROPERTIES OF BINOMIAL COEFFICIENTS

This leads to Pascal Triangle.


MULTINOMIAL FORMULA

where the sum, denoted by ∑, is taken over all non-negative integers nl, n2, . . .,np for which

n1+n2+...+np=n