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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
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVFJREFU
WEftl4sNwyAMROnKrMMmzMEULOHaBMgPiGlQ40ggRVUFmJfjbMgHsKk3NgJ/Y1NvhA4uEQHuLWil
wfoCTaXveXBnKMfwKYA3+p4HDyI7MDXFK30T/F6uTMXv6dc/eyrer9m9GW9UPBwwVMeXx7iNBI0+
IeWwf7+GgCe1uL/9mOcZCtKxqi0sVwXyG25b/j9imfExouIerKa7AkEbRJffslW81Zgcv0FzLZLG
JVl6523nrx6nDBZuj60PMrhDxat3YoHOCeBkE6qfzsQ6igm7q6fLIFEvRp/JoNOnR6owR+rWZX/g
bpBwR9+fBIzrddTx1rE8gB531O7KWap05diCwH08RyLoRbGQA34QlvIuW7ggulDwtk3oPWSCM84U
keBXNhGq+LVN+OCty/6ASrgLwbAJH3w0XCMexyYiwbkadSQnN+R/xk3w/+i8rvIFKTM8M+C8q50A
AAAASUVORK5CYII=
)
.
(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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