Multinomial Theorem Proof. When k 1 k 1 k 1 the result is true and when k 2 k 2 k 2 the result is the binomial theorem. 3 3 multinomial theorem theorem 3 3 0 for real numbers x1 x2 xm and non negative integers n r1 r2 rm the followings hold.
Since this can be rewritten as. X1 x2 xm n σ n r1 rm 1. 3 3 multinomial theorem theorem 3 3 0 for real numbers x1 x2 xm and non negative integers n r1 r2 rm the followings hold.
First for m 1 both sides equal x 1 n since there is only one term k 1 n in the sum.
3 3 multinomial theorem theorem 3 3 0 for real numbers x1 x2 xm and non negative integers n r1 r2 rm the followings hold. The algebraic proof is presented first. When k 1 k 1 k 1 the result is true and when k 2 k 2 k 2 the result is the binomial theorem. This is called the multinomial formula.
