(1) binomial theorem

(a+b) n = cn0an+cn 1 an-1b+…+cnran-rbr+…+CNN (the display here is a bit out of line, I believe you can understand it), where r = 0,1,2, …, n, n.

Its extended general term is:

Tr+ 1=cnran-rbr(r=0， 1，…n)，

The binomial remainder of its expansion is cnr(r=0, 1, …n).

(2) the nature of binomial remainder

(1) In binomial expansion, binomial residues with the same head-to-tail distance are equal, that is, CNR = CNN-R (r = 0, 1, 2 … n) (2) is cnr≥cnr- 1.

cnr≥cn+ 1r

get(n- 1)/2≤R ≤( n+ 1)/2。

When n is an even number, the central term of its expansion is TN/2+ 1, and the binomial remainder cnn/2 is the largest.

When n is an odd number, the middle two terms in the expansion are t (n+ 1)/2+ 1 and t (n+ 1)/2, and the binomial coefficient is cn(n- 1)/2 (or cn(n

The biggest.

③ the relationship between binomial coefficients of two adjacent terms: CNR+1= (n+r)/(r+1) CNR (r ≤ n, n ∈ n, r ∈).

④ sum of all binomial coefficients of binomial expansion: CN0+CN 1+CN2+…+CNN = Zn,

⑤ In binomial expansion, the sum of binomial coefficients of odd terms is equal to the sum of binomial coefficients of even terms:

cn0+cn2+cn4+…= cn 1+cn 3 1+cn5+…= 2n- 1