已知Ix-2I+Iy-4I=0求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+Y+2010)

问题描述:

已知Ix-2I+Iy-4I=0求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+Y+2010)

∵Ix-2I+Iy-4I=0,∴x=2,y=4 ; ∴1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+Y+2010) =1/2*4+1/4*6+1/6*8+……+1/2012*2014 =(1/2-1/4)/2+(1/4-1/6)/2+(1/6-1/8)/2+……+(1/2012-1/2014)/2 =(1/2-1...