题干

如图,将一条长度为1的线段三等分,然后取走其中的一份,称为第一次操作;再将余下的每一条线段三等分,然后取走其中一份,称为第二次操作;…如此重复操作,当第n次操作结束时,被取走的所有线段长度之和为 ____


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同类题4

    A famous study was done in a school by a professor from a university. At the start of the school year, the teachers were given the names of five children. They were told that these five were the most excellent students in the class. But the fact was that these students were only average, and they were not the best students at all. Well, guess what? At the end of the year, all the five average students scored among the highest in the class.
 What made these average students change so much to become top students? The only difference was the change in their teachers' attitude. Because the teachers believed that these five kids were the top students, they expected more from them. And so these five average students began to believe and expect more from themselves. So they worked harder to do as well as they could.
 Do you know why? If you expect the best from people, they'll usually want to give you their best. A great leader said, “Treat a person just how he appears to be on the outside, and you'll make him even worse. But treat a person like he's already a success, and you'll help make him the best he can be.”
 Like the true story of 7-year-old Johnny, his teacher got so angry with him that one day she said,“Johnny, you're the naughtiest boy in this class. I'm sure you'll never change.” The next year Johnny had a new teacher. And on the first day of class, she met with Johnny after school and said,“Johnny, I've heard a lot about you! But do you know that I don't believe a word of it.” And every day after that, this new teacher treated Johnny as if he was one of the smartest students even when Johnny did naughty things. Later on, Johnny became a school leader. Because that's the power of our belief and attitude toward children.