已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/25 17:19:40
已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?
x){}K+l u*mt +* 5* 55,M1փr " &H*PE}57573ڏk`` ,l Q `~qAb}6` eHPfAB`  Iiiui<ܳΆ'>iM POPտb

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)=?

已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?
原式=1/1-1/2+1/2-1/3+……+1/2008-1/2009
=1-1/2009
=2008/2009

因为:1/(2*1)=1/1-1/2 1/(2*3)=1/2-1/3 ……
1/n*(n-1)=1/(n-1)-1/n
所以有;1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.....+1/(x+2007)(y+2007)=
=1/1-1/2+1/2-1/3+……+1/2008-1/2009
=1-1/2009
=2008/2009

已知x+y=1,xy=-2,则x²y+xy²-2xy 已知xy/x+y=1/2,则代数式3x-5xy+3y/-x+3xy-y= 已知3/(x-y)=1/xy 求(-x-2xy+y)/ (2x+3xy-2y) 已知xy-x-y=11,求(xy-1)^2+(x+y-2)(x+y-2xy)的值. 已知x+y=-1,xy=-2,求代数式-5（x+y)+(x-y)+x(xy+y)的值 .已知:x-y=1,xy=-2.求:(-2xy+2 x+3y)-(3xy+2y-2x)-(x+4y+xy)的值 已知x(x-1)-(x²-y)=-3,求(x²y+xy²)÷xy-2y 已知x y=1,xy=-3,求2xy-4x 4(y-2(xy-x)) 已知x+y=1,xy=1/5,则x^2y=xy^2 已知x+y=-1,xy=-2,求代数式-5（x+y)+(x-y)+2(xy+y)的值 已知x-y=3,xy=1,求（-2x+2x+3y)-(3xy+2y-2x)-(x+4y+xy) 已知xy>0,证明xy+xy/1+x/y+y/x>=4 已知x(x-1)-(x^2-y)=-3.求x^2+y^2-2xy 已知x(x+1)-(x²+y)=3求2/x²+y²-xy 已知x平方+y平方+2xy+1=2x+2y,求x+y 已知x平方+y平方-2xy-2x-2y=-1,求x+y 已知x>y>0,xy=1,求x^2+y^2/x-y的最小值. 已知x,y,z∈R,求证:x^2+y^2>=xy+x+y-1