用等价无穷小的定义直接得出了因为lim(1+x)^a/(1+ax)=1(x→0)所以(1+x)^a与1+ax等价无穷小(x→0)so(1+x)^a-1等价于ax也可以用迈克劳林展开式的:(1+x)^a=1+a*x+1/2*a*(a-1)*x^2+1/6*a*(a-1)*(a-2)*x^3+1/24*a*(a-1)*(a-2)*(a-3)*x^4+1/120*a*(a-1)*(a-2)*(a-3)*(a-4)*x^5