已知(ab-2)*(ab-2)+|b-1|=0求:1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 02:36:10
已知(ab-2)*(ab-2)+|b-1|=0求:1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)的值

已知(ab-2)*(ab-2)+|b-1|=0求:1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)的值
已知(ab-2)*(ab-2)+|b-1|=0求:1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)的值

已知(ab-2)*(ab-2)+|b-1|=0求:1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)的值
(ab-2)*(ab-2)+|b-1|=0,
ab-2=0,b-1=0
b=1,a=2.
1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)
=1/2*3+1/3*4+.+1/2012*2013
=1/2-1/3+1/3-1/4+.+1/2012-2013
=1/2-1/2013
=2011/4026

(ab-2)²+|b-1|=0
ab-2=0 b-1=0 b=1
a-2=0 a=2
1/(a+1)(b+1)+1/(a+2)(b+2)+....+1/(a+2011)(b+2011)
=1/3×2+1/4×3+....+1/2013×2012
=1/2-1/3+1/3-1/4+....-1/2012+1/2012-1/2013
=1/2-1/2013
=2011/4026

a=2,b=1
裂项求和,所以值为2011/4026