x[(1-x)+(1-x)^2+(1-x)^3+…+(1-x)^50]
=[1-(1-x)]*[1+(1-x)+(1-x)^2+(1-x)^3+…+(1-x)^50-1]
=1-(1-x)^51-x
=1-x+(x-1)^51
所以要算原式中x^4的系数,只要算上式中x^5的系数:
C(51,46)*(-1)^46=C(51,5)=2349060
x[(1-x)+(1-x)^2+(1-x)^3+…+(1-x)^50]
=[1-(1-x)]*[1+(1-x)+(1-x)^2+(1-x)^3+…+(1-x)^50-1]
=1-(1-x)^51-x
=1-x+(x-1)^51
所以要算原式中x^4的系数,只要算上式中x^5的系数:
C(51,46)*(-1)^46=C(51,5)=2349060