已知b-1的相反数等于他本身,ab与-2互为相反数求1/ab+1/(a+1)(b+1)+.+1(2009+a)(2009+b)的值_数学解答

已知b-1的相反数等于他本身,ab与-2互为相反数求1/ab+1/(a+1)(b+1)+.+1(2009+a)(2009+b)的值

人气：465 ℃　时间：2020-01-30 22:34:19

解答

b-1=1-b
b=1
ab-2=0
a=2
1/ab+1/(a+1)(b+1)+.+1(2009+a)(2009+b)
=1/1x2+1/2x3+1/3x4+...+1/2010x2011
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2010-1/2011)
=1-1/2011
=2010/2011