1+c(n, 1)x+c(n,2)x^2+...+C(n,n)x^n

Let x= 1 and the equation holds.

Let x=- 1, and we get

1-C(n， 1)+C(n，2)+...+C(n,n)(- 1)^n=0

Subtract the current equation from the previous equation, divide both sides by 2, and the sum of even terms is 2 (n- 1).