数学题 1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=？要步骤！

显示全部楼层 · 2011-9-25 20:00:42

1×1/2=1/2=1-1/21/2×1/3=1/6=1/2-1/31/3×1/4=1/12=1/3-1/4......................................1/2005×1/2006=1/2005-1/2006所以1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=1-1/2+1/2-1/3+1/3-1/4+............+1/2005-1/2006=1-1/2006=2005/2006...

千问 · 2011-9-25 20:00:42

1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=(1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/2005-1/2006)=1-1/2006=2005/2006...

千问 · 2011-9-25 20:00:42

原式=1-1/2+1/2-1/3+1/3-1/4……+1/2005-1/2006
=1-1/2006
=2005/2006...

数学题 1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=？ 要步骤！

数学题 1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=？要步骤！