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已知曲线C:xy=1,过C上一点An(xn,yn)作一斜率为的直线交曲线C于另一点An+1...
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已知曲线C:xy=1,过C上一点A
n(x
n,y
n)作一斜率为
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAqCAYAAADlL5amAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
的直线交曲线C于另一点A
n+1(x
n+1,y
n+1),点列A
n(n=1,2,3,…)的横坐标构成数列{x
n},其中
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAjCAYAAADrJzjpAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFYSURBVFhH7ZeBDYQgDEWZjJ1Yh2UYhVF6VIFT
D0oR4tUEE3MxtPDu8ymg4KWPeik3LPChmfMWtNJgfaGXStv/FXcGlFLhLYATbf8H30R2YGqKV9oW
+JDHl+Jj8t3IXh6/IdpQyhsV3zYYrOP7a9xBAaJtWjlMA3N+hyYnJk8DnwHT04eCtK1qC/tRAf0W
pi1/93T3XGxU3IPVeFZAaBPQ5T/ZKt7qsDjuQ3O8nWKSLD05x1jM/3ocV7Bwexx9kMFdULx6Jhbo
nA0cbYL105lYR8OCPdVTieDoHZ2uHqnClKipW8rEP4biXb1fwuHVceqWMhE6TD3YU0lL1e53EB54
ru+Ve+EseO/jXhI7JAqGLPCLALj2so0vbYLB6zY51/HmdFNHz2Zyf0BjXxGrOGUTwYrTNpELzjh+
8KxC3VL63dvMaNmkU/HmeI8G8BR/FIk32ALn6TQv6gOFOtOgT3oUWAAAAABJRU5ErkJggg==
)
.
(1)求x
n与x
n+1的关系式;
(2)求证:{
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACwAAAAqCAYAAADI3bkcAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
}是等比数列;
(3)求证:(-1)x
1+(-1)
2x
2+(-1)
3x
3+…+(-1)
nx
n<1(n∈N,n≥1).
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