解1/1*2=1/1-1/21/2*3=1/2-1/31/3*4=1/3-1/4.1/2008*2009=1/2008-1/2009上述各式相加的1×2分之1加2×3分之1加3×4加省略号加2008×2009分之1=1/1-1/2+1/2-1/3+1/3-1/4+.+1/2008-1/2009=1/1-1/2009=2008/2009...