The numbers 1/1,1/2,…..,1/2010 are written on a blackboard.A

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The numbers 1/1,1/2,…..,1/2010 are written on a blackboard.A student chooses any two of the numbers,say x ,y,erases them and then writes down x+y+xy.He continues to do this until only one number is left on the blackboard.What is this number?

2010
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再答：意思是在黑板上有一串数字，从1/1,1/2,1/3,1/4……1/2010，一个学生选择其中的两个，赋值为x,y，擦掉它们两个并写下另一个数字，该数字= x+y+xy。他按照这种方式一直进行下去，直到黑板上最终只剩下一个数字，这个数字是多少？我按照最简单的方式算，假设该学生最先选的是1/1和1/2，那么x=1/1，y=1/2，x+y+xy=1+1/2+1/2=2。这时擦掉1/1和1/2，写下数字2。然后再选择2和1/3，那么此时x+y+xy=2+1/3+2×1/3=3。再擦掉2和1/3，写下4,。再选4和1/5，得出数字5,……以此类推，最终得到数字2010。.

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