依题意
a-1=0
ab-2=0
由此得到
a=1,b=2
代入
1/2+1/(2*3)+1/(3*4)+.+1/(2007*2008)+1/(2014*2015)
=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008+1/2014-1/2015
=1-1/2015
=2014/2015