根据题意得
ab-2=0
1-b=0
∴a=2
b=1
∴原式=1/1×2+1/2×3+1/3×4+……+1/2013×2014
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2013-1/2014
=1-1/2014
=2013/20141/1-1/2+1/2-1/3+1/3-1/4+……+1/2013-1/2014
这部步骤不明白，能详细点么？1/1×2
=(2-1)/1×2
=2/1×2 -1/1×2
=1-1/2
其它类似
再如
1/2013×2014
=(2014-2013)/2013×2014
=2014/2013×2014-2013/2013×2014
=1/2013-1/2014