设直线KX+(K+1)Y-1=0(K>0)与坐标围成的直角三角形的面积为Sk,求S1+S2+ +S2004

KX+(K+1)Y-1=0(K>0)
当X=0时,Y=1/(K+1)
当Y=0时,X=1/K
Sk=1/2*1/(K+1)*1/K=1/2*1/K(K+1)
S1+S2+ ……+S2004
=1/2(1/1*2+1/2*3+1/3*4+……+1/2004*2005)
=1/2(1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005)
=1/2(1-1/2005)
=1002/2005