从点P1(1，0)作x轴的垂线，交抛物线y=x2于点Q1(1，1)；再从Q1作这条抛物线的切线与x轴交于P2，然后又从P2作x轴的垂线，交抛物线于点Q2，依次重复上述过程得到一系列的点P1，Q1；P2，Q2；…；PnQn；…．
(1) 求
；
(2) 求级数
为自然数，而
表示点Qi与Pi之间的距离．
参考答案：依题意画图(如图)．由y=x2得y’=2x，任给a(0＜a≤1)，抛物线y=x2在点(a，a2)处的切线方程为y-a2=2a(x-a)，该切线与x轴的交点为[*]，因此由[*]．可知
[*]
以此类推，知[*]
(2) 又由[*]，知级数
[*]
[*]
解析：[考点提示] 切线方程、级数求和．
完形填空。（共12分，每小题1分） 阅读下面的短文，掌握其大意，然后从短文后各题所给的A、B、C、D 四个选项中，选择最佳选项。 Eleven-year-old Angela had something wrong with her nervous system（神经系统）.She was unable to __1__. In fact, she could hardly make any __2_. Although she believed that she had a good chance of recovering, the doctors said that __3__ , if any, could come back to normal after getting this disease. Having heard this, the little girl was not discouraged. There, lying in her hospital bed, she insisted that no matter what the doctors said, her going back to school was __4__. She was moved to a specialized health center, and whatever method could be tried was used. Still she would not __5__. It seemed that she was undefeatable(打不败的). The doctors were all fond of her and taught her about __6_ that she could make it . Every day Angela would lie there, faithfully doing her mental exercise. One day, __7__ she was imagining her legs moving again, it seemed as though a miracle（奇迹）happened: The bed began to move! “Look what I’m doing! Look! I can do it! I moved! I moved! ”she shouted___8___! Of course, at this very moment everyone else in the hospital was __9__. More importantly, they were running __10__ safety. People were crying, and equipment was falling .You see, it was an___11___. But don’t tell that to Angela. She has believed that she did it, just as she had never doubted that she would recover. And now only a few years later, She’s back in school. You see, to such a person who can __12__ the earth, such a disease is a small problem, isn’t it?
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