f(x)=(x-1)/(4-x)=(x-4+3)/(4-x)=-1+3/(4-x)=-1+3/[3-(x-1)]=-1+1/[1-(x-1)/3]公比是(x-1)/3的等比级数：f(x)=-1+1+(x-1)/3+(x-1)²/3²+...+（x-1）^k/3^k+....=(x-1)/3+(x-1)²/3²+...+（x-1）^k/3^k+....f^(n)(1)=n!/3^n
