1乘1/2+1/2乘1/3+1/3乘1/4+.+1/2009乘1/2010等于?

1/(1*2) + 1/(2*3) + 1/(3*4) +.+ 1/(2009*2010) = (1-1/2) + (1/2 - 1/3) + (1/3 - 1/4) + .+ (1/2009 - 1/2010) = 1-1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .+ 1/2009 - 1/2010 = 1 +(-1/2 + 1/2) + ( - /3 + 1/3) + ( -1/4 + .+ 1/2009) - 1/2010 = 1 - 1/2010 = 2009/2010