1/1×2+1/2×3+1/3×4…1/2008×2009+1/2009×2010﹦?简算

问题描述:

1/1×2+1/2×3+1/3×4…1/2008×2009+1/2009×2010﹦?简算

1/1×2+1/2×3+1/3×4…1/2008×2009+1/2009×2010
=1-1/2+1/2-1/3+1/3-1/4+.+1/2008-1/2009+1/2009-1/2010
=1-1/2010
=2009/2010