lgf(x)=lgx+lg(x+1)+...lg(x+100)f'(x)/f(x)=1/x+1/(x+1)+..+1/(x+100)f'(x)=f(x)[1/x+1/(x+1)+...+1/(x+100)] =(x+1)...(x+100)+f(x)[1/(x+1)+..+1/(x+100)]f'(0)=100!+0=100!