若〡x1-1〡+(x2-2)^2+〡x3-3〡^3+(x4-4)^4+…+〡x1999-1999〡^1999+(x2000-2000)^2000=0,求1/x1x2+1/x2x3+1/x3x4+…+1/x1999x2000的值.还问什么?、
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![若〡x1-1〡+(x2-2)^2+〡x3-3〡^3+(x4-4)^4+…+〡x1999-1999〡^1999+(x2000-2000)^2000=0,求1/x1x2+1/x2x3+1/x3x4+…+1/x1999x2000的值.还问什么?、](/uploads/image/z/8556756-60-6.jpg?t=%E8%8B%A5%E3%80%A1x1-1%E3%80%A1%2B%EF%BC%88x2-2%29%5E2%2B%E3%80%A1x3-3%E3%80%A1%5E3%2B%28x4-4%29%5E4%2B%E2%80%A6%2B%E3%80%A1x1999-1999%E3%80%A1%5E1999%2B%28x2000-2000%29%5E2000%3D0%2C%E6%B1%821%2Fx1x2%2B1%2Fx2x3%2B1%2Fx3x4%2B%E2%80%A6%2B1%2Fx1999x2000%E7%9A%84%E5%80%BC.%E8%BF%98%E9%97%AE%E4%BB%80%E4%B9%88%EF%BC%9F%E3%80%81)
若〡x1-1〡+(x2-2)^2+〡x3-3〡^3+(x4-4)^4+…+〡x1999-1999〡^1999+(x2000-2000)^2000=0,求1/x1x2+1/x2x3+1/x3x4+…+1/x1999x2000的值.还问什么?、
若〡x1-1〡+(x2-2)^2+〡x3-3〡^3+(x4-4)^4+…+〡x1999-1999〡^1999+(x2000-2000)^2000=0,求1/x1x2+
1/x2x3+1/x3x4+…+1/x1999x2000的值.
还问什么?
、
若〡x1-1〡+(x2-2)^2+〡x3-3〡^3+(x4-4)^4+…+〡x1999-1999〡^1999+(x2000-2000)^2000=0,求1/x1x2+1/x2x3+1/x3x4+…+1/x1999x2000的值.还问什么?、
数列题最重要看是什么数列
自己想
∵|x1-1|+|x2-2|^2+|x3-3|^3+······+|x2000-2000|^2000=0,
∴x1=1、x2=2、x3=3、x4=4、x5=5、······、x2000=2000,
∴1/(x1x2)+1/(x2x3)+1/(x3x4)+1/(x4x5)+······+1/(x1999x2000)
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×...
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∵|x1-1|+|x2-2|^2+|x3-3|^3+······+|x2000-2000|^2000=0,
∴x1=1、x2=2、x3=3、x4=4、x5=5、······、x2000=2000,
∴1/(x1x2)+1/(x2x3)+1/(x3x4)+1/(x4x5)+······+1/(x1999x2000)
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+······+1/(1999×2000)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+······+(1/1999-1/2000)
=1-1/2000
=1999/2000
这是我找到的正确答案
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