1 . 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).
、
、
为第一代龙曲线的顶点,设第
代龙曲线的顶点数为
,由图可知
,
,
,则
___________ ;数列
的前
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___________ .
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2022-01-25更新
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6卷引用:山西省吕梁市临县第一中学2022届高三上学期期末数学试题