若a-1=0,ab-2=0.求:1/ab+1/(a+1)(b+1)+......+1/(a+2000)(b+2000)的值
问题描述:
若a-1=0,ab-2=0.求:1/ab+1/(a+1)(b+1)+......+1/(a+2000)(b+2000)的值
答
a-1=0,ab-2=0
a=1
b=2/a=2
所以原式=1/1*2+1/2*3+……+1/2001*2002
=1-1/2+1/2-1/3+……+1/2001-1/2002
=1-1/2002
=2001/2002