设 (1+x)^100 = a0+a1x+a2x^2+a3x^3+...+a100x^100 ,那麼a0+a1+a2+a3+...+a100=?
问题描述：
设 (1+x)^100 = a0+a1x+a2x^2+a3x^3+...+a100x^100 ,那麼a0+a1+a2+a3+...+a100=?
设 (1+x)^100 = a0+a1x+a2x^2+a3x^3+...+a100x^100
那麼a0+a1+a2+a3+...+a99+a100=?
a0+a2+a4+a6+a8=?
答
(1+x)^100 = a0+a1x+a2x^2+a3x^3+...+a100x^100x=1时,a0+a1+a2+a3+...+a100= (1+1)^100 =2^100x=-1时,a0-a1+a2-a3+a4-a5+...-a99+a100= (1-1)^100 =0上面两式相加,得2(a0+a2+a4+...+a100)=2^100所以a0+a2+a4+...+a10...