一道裂项题1/2*4+1/4*6+1/6*8+...+1/2008+2010下面的图片不知道能不能看清,看不清就看我写的

1/(2*4)+1/(4*6)+1/(6*8)+...+1/(2008*2010)
=(1/2)*[2/(2*4)+2/(4*6)+...+2/(2008*2010)]
=(1/2)*[(1/2-1/4)+(1/4-1/6)+...+(1/2008-1/2010)]
=(1/2)*(1/2-1/2010)
=167/335