x=2,y=1,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2010)(y+2010)=

lover7711272022-10-04 11:39:543条回答

x=2,y=1,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2010)(y+2010)=?

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我就晕共回答了18个问题 | 采纳率88.9%: 先说明一个公式：1/n(n+1)=1/n-1/(n+1)
这个公式通分就可以证明
把x,y代进去
1/1*2+1/2*3+1/3*4+…………+1/2011*2012
=1/1-1/2+1/2-1/3+1/3-1/4+…………+1/2011-1/2012
=2011/2012; 1年前

cpp2121 共回答了37个问题 | 采纳率: 1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2010)(y+2010)
=1/1*2+1/2*3+1/3*4+......../2011*2012
=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+.....(2012-2011)/2011*2012)
=1-1/2+1/2-1/3+1/3+.....-2011/2012
=1/2012; 1年前

abmm7 共回答了74个问题 | 采纳率: 1=x-y
1/(x+n)(y+n)=[(x+n)-(y+n)]/(x+n)(y+n)=1/(y+n)-1/(x+n)
原式=(1/1-1/2)+(1/2-1/3)+...+(1/2011-1/2012)=1-1/2012=2011/2012; 1年前

x-1的绝对值+（xy-2)平方=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+20 x-1的绝对值+（xy-2)平方=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2008)(y+2008)= dyx_20061年前1: 青天大老爷共回答了18个问题 | 采纳率100%

x-1的绝对值+（xy-2)平方=0
x-1的绝对值和（xy-2)平方均为非负数,现在和为0,则均为0
有：x-1=0
xy-2=0
x=1
y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2008)(y+2008)=
=1/1*2+1/2*3+..+1/2009*2010
=1-1/2+1/2-1/3+...+1/2009-1/2010
=1-1/2010
=2009/2010
补充：1/1*2=1-1/2
1/2*3=1/2-1/3
...
1/2009*2010=1/2009-1/2010

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已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007 已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=? 54485691年前2: 凡人0506 共回答了14个问题 | 采纳率100%

原式=1/1-1/2+1/2-1/3+……+1/2008-1/2009
=1-1/2009
=2008/2009

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已知x-1的绝对值与y-2的绝对值互为相反数,计算1/xy+1/(x+1)（y+1)+1/(x+2)(y+2)+ zerory1年前3: 属鼠共回答了17个问题 | 采纳率94.1%

x=1 y=1代入就好了

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因为绝对值和平方的结果都不小于0,因此只有两部分都为0时才成立
X-1=0,X=1
XY-2=0,XY=2,Y=2
1/（1×2）=1/1-1/2,1/（2×3）=1/2-1/3,1/（3×4）=1/3-1/4...
所以
原式=1/（1×2）+1/（2×3）+1/（3×4）+...+1/（2012×2013）
=1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013
=1-1/2013
=2012/2013

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当X=1,Y=2时,那么……1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+2009)(y 当X=1,Y=2时,那么…… 1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+2009)(y+2009)=_____ zxc11年前1: xiaoff101 共回答了21个问题 | 采纳率95.2%

＝1+1/2-1/3+...+1/2010-1/2011
=1-1/2011
=2010/2011

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x^2+y^2-2x-4y+5=0
则(x-1)^2+(y-2)^2=0
x=1,y=2
原式＝1/(1*2)+1/(2*3)+.+1/(n*(n+1))+.+1/(2010*2011)
＝1/1-1/2+1/2-1/3+.+1/n-1/(n+1)+.+1/2009-1/2010+1/2010-1/2011
＝1-1/2011＝2010/2011

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xy-2=0,y-1=0
xy=2,y=1
x=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2).1/(x+2014)(y+2014)
=1/1*2+1/2*3+.+1/2015*2016
=1-1/2+1/2-1/3+.+1/2015-1/2016
=1-1/2016
=2015/2016

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