如图所示,在著名的汉诺塔问题中,有三根高度相同的柱子和一些大小及颜色各不相同的圆盘,三根柱子分别为起始柱、辅助柱及目标柱.已知起始柱上套有
个圆盘,较大的圆盘都在较小的圆盘下面.现把圆盘从起始柱全部移到目标柱上,规则如下:每次只能移动一个圆盘,且每次移动后,每根柱上较大的圆盘不能放在较小的圆盘上面,规定一个圆盘从任一根柱上移动到另一根柱上为一次移动.若将
个圆盘从起始柱移动到目标柱上最少需要移动的次数记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f9735c4c32ba04c6524719918c7681.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32f7f3f4bc99b591c5b9177418c5eba.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006d54905e72dac6b9f6fcf1a6ada6d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f9735c4c32ba04c6524719918c7681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32f7f3f4bc99b591c5b9177418c5eba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/2c7ca0e0-f024-47f5-abaf-605ed99d7b58.png?resizew=228)
更新时间:2020-04-27 14:31:18
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【推荐1】观察下列式子,
,
,
,……,根据上述规律,第
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【推荐2】观察下列各式:
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……
照此规律,当n
N时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383862c507949500ce2271feb88217b4.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7c576900cb8b22afc47596301f0e75.png)
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……
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