设曲线y=xn+1（n∈N*）在点（1，1）处的切线与x轴的交点的横坐标为xn，令an=lgxn，则a1+a2+…+a99的值为______．
对y=xn+1（n∈N*）求导得y′=（n+1）xn，
令x=1得在点（1，1）处的切线的斜率k=n+1，在点
（1，1）处的切线方程为y-1=k（xn-1）=（n+1）（xn-1），
不妨设y=0，xn=
| n |
| n+1 |
则x1•x2•x3…•xn=
| 1 |
| 2 |
| 2 |
| 3 |
| 3 |
| 4 |
| n-1 |
| n |
| n |
| n+1 |
| 1 |
| n+1 |
从而a1+a2+…+a99
=lg（x1•x2•x3…•x99）
=lg
| 1 |
| 100 |
故答案为：-2．
任务型阅读 (共10小题; 每小题1分, 满分10分) One of the most well-known directors of our time is Stephen Spielberg. He was born in Cincinnati on 18 December 1946. His father was an electric engineer and his mother was a performing pianist. His sister, Anne Spielberg, became a screenwriter who wrote the stories for many famous films. Stephen had always wanted to be a director ever since he was a young boy. When he was just 13 years old, he made a 40-minute film. It won a local competition. Three years later, he produced a film called Firelight, which made one hundred dollars’ profit at the cinema in his hometown. Many of the ideas from this film were later used for one of his most famous films called Close Encounters of the Third Kind. When he was 18 years old, he wanted to go to film school so that he could improve his skills and become an even better director. Unluckily, he was unsuccessful in getting a place at this school so he went to a university in California to study English. Even though he had failed to get into the school he wanted to go to, he didn’t let this stop him following his dream to become a great director. Stephen Spielberg has directed many films since his first major film in 1976. He now owns many different businesses, most of which are involved in the film industry.
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