利用列项求和
2/1×2＋2/2×3＋2/3×4＋…＋2/2008×2009＋2/2009×2010
=2(1-1/2)+2(1/2-1/3)+2(1/3-1/4)+...+2(1/2008-1/2009)+2(1/2009-1/2010)
=2(1-1/2+1/2-1/3+...+1/2009-1/2010)
=2(1-1/2010)
=2*2009/2010
=2009/1005