解答:
y=x^(n+1)
则y'=(n+1)*x^n
∴ 切线斜率k=n+1
∴ 切线方程是y-1=(n+1)*(x-1)
y=0,则 x-1=-1/(n+1)
即 x=1-1/(n+1)=n/(n+1)
∴ xn=n/(n+1)
∴ a1+a2+a3+....+a99
=lg(1/2)+lg(2/3)+lg(3/4)+.....+lg(99/100)
=lg[(1/2)*(2/3)*(3/4)*......*(99/100)]
=lg(1/100)
=-2
追答lg(1/100)=lg(10^(-2))=-2lg10=-2*1=-2