Multinomial Expansion Formula. For any positive integer m and any non negative integer n the multinomial formula tells us how a sum with m terms expands when raised to an arbitrary power n. The greatest coefficient in a multinomial expansion.
For any positive integer m and any non negative integer n the multinomial formula tells us how a sum with m terms expands when raised to an arbitrary power n. Formula the greatest coefficient in the expansion of a1 a2 a3 am n is q m r q 1. 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.
Write down the squares.
For a positive integer. In particular the expansion is given by where n 1 n 2 n k n and n. X 1 x 2 x m n k 1 k 2 k m n n k 1 k 2 k m t 1 m x t k t displaystyle x 1 x 2 cdots x m n sum k 1 k 2 cdots k m n n choose k 1 k 2 ldots k m prod t 1 m x t k t. Is the factorial notation for 1 2 3 n.
