Multinomial Theorem Example. For example the bottom n 5 expansion has 6 terms the powers of x start at n and decrease by 1 in each term until they reach 0. Multinomial theorem for a positive integer k k k and a non negative integer n n n x 1 x 2 x k n b 1 b 2 b k n n b 1 b 2 b 3 b k j 1 k x j b j.
6 2 1 1 3. Nk such that n1 n2. It is possible to read off the multinomial coefficients from the terms by using the multinomial coefficient formula.
Left x 1 x 2 cdots x k right n sum b 1 b 2 cdots b k n binom n b 1 b 2 b 3 ldots b k prod j 1 k x j b j.
The binomial multinomial theorems. For example in the bottom n 5 expansion the coefficients 1 5 10 10 5 and 1 add up to 2 5 32. Multinomial theorem for a positive integer k k k and a non negative integer n n n x 1 x 2 x k n b 1 b 2 b k n n b 1 b 2 b 3 b k j 1 k x j b j. The powers of y start at 0 and increase by 1 until they reach n.
