已知|a-2|和|b-1|互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 18:17:25
已知|a-2|和|b-1|互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值

已知|a-2|和|b-1|互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值
已知|a-2|和|b-1|互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值

已知|a-2|和|b-1|互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值
即|a-2|+|b-1|=0\
所以a-2=b-1=0
a=2,b=1
原式=1/1*2+1/2*3+……+1/2010*2011
=1-1/2+1/2-1/3+……+1/2010-1/2011
=1-1/2011
=2010/2011

|a-2|和|b-1|互为相反数
a-2=0 b-1=0
a=2 b=1
求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
=1/1*2+1/2*3+1/3*4+...+1/2010*2011
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011
=1-1/2011
=2010/2011