2/1X2+2/2X3+2/3X4……+2/2008X2009等于多少

网友回答

2/1X2+2/2X3+2/3X4……+2/2008X2009
=2×（1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009）
=2×（1-1/2009）
=2-2/2009
=1又2007/2009
======以下答案可供参考======
供参考答案1:
2/1X2+2/2X3+2/3X4……+2/2008X2009
=2*(1/1X2+1/2X3+1/3X4……+1/2008X2009)
=2*[(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+（1/2008-1/2009)]
=2*(1-1/2009)
=4016/2009
供参考答案2:
2X(1-1/2009)=4016/2009