计算:1/(1×2)+1/(2×3)+1/(3×4)+.+1/(2009×1010)

问题描述:

计算:1/(1×2)+1/(2×3)+1/(3×4)+.+1/(2009×1010)

=1-1/2+1/2-1/3+1/3-1/4+.+1/2009-1/2010
=1-1/2010
=2009/2010