已知数列
的各项都为正数,前
项和为
,若
是公差为1的等差数列,且
,
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933114ff9d61b7afbd0f26ccaf0a59d1.png)
_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2435fe06ff53f87ae3070c01b43b4a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a85a39010b04d1fe20d3bb9faf7ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558ee10caedbd89684fc842d33eb58b7.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933114ff9d61b7afbd0f26ccaf0a59d1.png)
更新时间:2018-03-21 10:05:23
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【推荐1】在数列
中,
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【推荐2】南宋数学家杨辉在《详解九章算法》和《算法通变本末》中,提出了一些新的垛积公式,所讨论的高阶等差数列与一般等差数列不同,前后两项之差不相等,但是逐项差数的差或者高次差成等差数列.如数列1,3,6,10,前后两项之差得到新数列2,3,4,新数列2,3,4为等差数列,这样的数列称为二阶等差数列,对这类高阶等差数列的研究,后人一般称为“垛积术”,现有高阶等差数列
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【推荐1】谢尔宾斯基三角形(Sierppinskitriangle)是一种分形,由波兰数学家谢尔宾斯基在1915年提出.先取一个实心正三角形,挖去一个“中心三角形”(即以原三角形各边的中点为顶点的三角形),然后在剩下的小三角形中又挖去一个“中心三角形”,我们用白色三角形代表挖去的面积,那么黑色三角形为剩下的面积(我们称黑色部分为谢尔宾斯基三角形).用上面的方法可以无限操作下去,操作1次得到第2个图案,操作2次得到第3个图案……,若最大的三角形边长为2,则操作4次后得到的第5个图案中挖去的白色三角形个数为___________ ,挖去的面积为___________ .
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【推荐2】龙曲线是由一条单位线段开始,按下面的规则画成的图形:将前一代的每一条折线段都作为这一代的等腰直角三角形的斜边,依次画出所有直角三角形的两段,使得所画的相邻两线段永远垂直(即所画的直角三角形在前一代曲线的左右两边交替出现).例如第一代龙曲线(图1)是以
为斜边画出等腰直角三角形的直角边
、
所得的折线图,图2、图3依次为第二代、第三代龙曲线(虚线即为前一代龙曲线).
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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